Im with a few others here when I don't believe in the tem "Cull Buck". It sounds like your shooting a deer just to get it out of the herd and your getting no enjoyment out of it. I refer to a deer like that as one that has reached his potential, just not a cull buck.
I think this deer will be fine for a few more years. If he has lived this long then his wound has healed. The only predator suburb deer face is ones with V8's! Ive seen a few 3 legged deer in my day and all look they have been doing fine.
Im not sure how hold this guy is. If he's 2 1/2, just take a look at his left side. If it wasnt for his injury then his right side would look the same. Thats not a horrible looking 2 1/2 year old. He'll grow some more, but just will never be a typical deer.
I wouldn't worry about genetics. His injury is one that occured after birth, therefor he doesn't have genetics to pass that gene on. He'll pass on the genetics of what he was bred with and what the left side of his rack looks like.
If that was in front of me for my first deer, I would take him without a doubt. Any first deer is one to be proud of and this one is really unique. Id take him for a first deer just not as a cull buck. If you'd be proud to take him, then take him. Good Luck!