The ex-soldier was on holiday in America in 1998 when he broke his neck, which left him paralysed below the shoulders.
Determined to keep active, Mr Harrison joined the Yorkshire Lions wheelchair rugby team.
Spinal injury charity Regain bought him a specialist rugby chair and he has now been named captain of the team.
Mr Harrison, of Snapethorpe Gate in Lupset, will be raising money for the charity by hand cycling 450km across Cuba.
He will ride a three-wheeled cycle propelled by his arms rather than his legs over five days, starting today.
Mr Harrison, 49, said: “I started playing wheelchair rugby to regain as much of my life back as I could.
“I gained some arm movement during rehabilitation and wanted to carry on living an active lifestyle.
“I struggled to find any sporting activities suitable for my level of impairment but wheelchair rugby helped me do that.”
Mr Harrison will join 84 others riders including his personal assistant Sarah Papirnyk.
And to prepare for the challenge, Mr Harrison trained at Thornes Park Stadium, as well as cycling around the countryside.
He said: “I want to give something back to Regain and put every muscle I can still use into this challenge.
“I will be raising funds so they can go on supporting other people like me that have experienced similar life changing spinal injuries.”
Mr Harrison wore a superman costume while training in tribute to actor Christopher Reeve, who helped raise money for spinal cord research after breaking his neck 20 years ago.
Regain helps improves the independence of men and women who have become tetraplegic as a result of a sports or leisure injuries.
To donate, log onto www.justgiving.com/fasterfaster.