Joe's unusual middle name came from his grandfather, Horatio Cone Wickham, a Tompkins County, New York native who moved to Story County, Iowa to operate a farm with his wife, Paulina R. Malloy. He paid $1.25 per acre in 1855, a year which saw a population boom of settlers in central Iowa. Joe's father, born in 1877, was the second youngest of their 15 children. Horatio was very active in the community, especially with school affairs. The first public building there was called the Wickham School. Built about 1865, it had log seats and a dirt floor, with a motto on the wall of "Not how much, but how well" (see school). Horatio's interest in education was probably sparked by his association with Ezra Cornell, who co-founded Cornell University in 1865 just a few miles from Horatio's boyhood home. He even named one of his sons Ezra Cornell Wickham in 1874.

Though the threat of Indian attack had ebbed by the 1850s, Horatio and his family faced plenty of danger on the frontier prairie. One night, their horse became sick and they were stuck in their wagon on the open prairie miles from home. Pauline stayed in the wagon with a gun to guard their baby children from hungry bears and wolves, while Horatio walked home for another horse. The night passed without incident, but years later, after their daughter Henrietta Wickham moved to the Dakota Territory, it was a different story. A prairie fire broke out in 1889 and Henrietta fled with her two small children to a cave where she thought it was safe, but as the gigantic flames raged outside of the cave's entrance, Henrietta was smothered, though her actions saved the lives of her brood, who recovered from the ordeal.

Joe's father John graduated in 1904 from Iowa State College with a degree of Bachelor of Civil Engineering, C.E., and wrote a book called Municipal Engineering in Iowa that was published by his alma mater in 1909. He worked as city engineer of Ames, Iowa for a while, but in 1926 decided to switch from administrating arcane building codes in the Frost Belt for a job 1,440 miles away in the Florida sunshine, exploring uncharted swamps full of snakes, snapping turtles and alligators. He moved his large family to Brevard County to work as a surveyor on drainage and road projects. The county was mainly wilderness then with only a few dirt roads and a population of just 8,500 people.

Joe, now 14, attended Eau Gallie High School on Pineapple Avenue, graduating in a class of five in 1929. As the Great Depression hit, he hunted for giant loggerheads to keep his family fed and on budget. He first worked as a soda deliveryman, then joined his father as a surveyor. Joe's early assignments included a survey of the north county line, a survey of the route for A1A, and supervision of initial construction of the Naval Air Station on the Banana River. During the 1930s, he also worked as Eau Gallie�s fire chief.

After his father was killed in a car accident in St. Johns County, Florida in 1940, Joe helped his mom raise five younger brothers. Soon he joined the Navy Seabees and worked as Chief Carpenter to build airports and runways on Pacific islands during World War II. He was wounded during the war. In the Philippines, he helped residents of a newly liberated village to reassemble a church that they had dismantled piece-by-piece and hid in the mountains before the Japanese invaders swept in. While stationed in California, he met a woman named Bernice, who became his wife in 1946.

After returning home, Joe used his wartime experience to start Wickham Construction Company, where he could be found most weekday mornings by 6 a.m. In 1952, after a stint on the Eau Gallie City Council, Brevard County Commissioner Max Rodes asked Joe to run for the District 5 commission seat as a Democrat. (Running as a Democrat was a no-brainer because 92% of the electorate were registered as Democrats). After taking office, he became chairman of a one-man committee that constructed a dredge and launched it by the Eau Gallie causeway in November 1953, marking the start of the county's permanent mosquito control program that impounded local waterways where the notorious salt marsh mosquito bred. Joe once explained, "Back then, it took some mighty rugged people to live on the beach or Merritt Island because the mosquitoes would destroy you. You couldn't walk outside without some type of heavy clothing and usually a net over your face." Financing the dredge proved difficult, as powerful politicians tried to divert the funds for personal projects, but Joe was able to outmaneuver these rascals by establishing a special municipal tax district where tax payer money was spent only in the district where the taxes were paid. He served for 26 years on the county commission, including several terms as commission chairman. Joe skipped some terms to spend more time with his sons.

In the late 1950s, Joe built Wickham Road through undeveloped county land between two ranges, 36 and 37, that he knew about through his earlier surveys. His initiative surprised many old-timers, including some moonshiners whose still was bulldozed aside by Joe's road crew. For decades, the route was just a dirt trail through Duda farmland, but as the population exploded it became one of the county's most important roads, linking the communities of Melbourne, Suntree and Viera to I-95 (see road). He also played a major role in having a 1,548-foot bridge over Sebastian Inlet built in 1965 (see bridge). Located in neighboring Indian River County, the bridge is part of State Road A1A, an important coastal route vital to Brevard County's economy. Less populous Indian River County was not initially interested in building such an expensive bridge, but Joe was able to "sweeten the pot" by deeding valuable beachfront property to them.

Using his ties with the Navy, Joe was able to foster a close working relationship between the county's residents and its numerous federal facilities, including NAS-Banana River, Patrick AFB, the Kennedy Space Center, and Cape Canaveral AFS. Among the benefits were programs for the county to buy used military equipment, job opportunities at the facilities for civilians, and improved land purchase programs.

Joe served as Potentate of the Bahia Shriners in 1968. In 1986, he was appointed by Governor Bob Graham to the South Brevard Water Authority.

Joe also started Wickham Park by convincing developers to donate land to the project. The 391-acre public county park located at 2500 Parkway Drive, in the center of Melbourne, Florida was Joe's pride and joy (see park entrance). He donated some land himself and used his construction company to clear the site and add sand to the bottom of the lakes. The park features campgrounds, a disc golf course, a senior center, equestrian facilities, an archery range, a dog park, recreation trails, ball fields, event and picnic pavilions, a playground, and gator-free swimming. It is one of just a few Wickham Parks in the world, including ones in Manchester, Connecticut and Brisbane, Australia. The one in Connecticut is named after Joe's fourth cousin Clarence Horace Wickham, an industrialist who invented the window envelope, while the one in Australia is named after John Clements Wickham, a more distant cousin who sailed with Charles Darwin aboard the HMS Beagle.