On 2 of 3 of my dispatched deer I didn't have a weapon, one was a next day tracking job that I didn't expect to find but did, he was in pretty bad shape but could get up and move a few feet before falling back down.
Another was a road struck deer I saw hit in the opposite lane, it was paralyzed from the mid back down. I was actually coming home from hunting, saw the deer get hit, pulled it out of the road, stabbed it, backed up to it with my deer hoist in place, loaded it and took it home, perfectly legal where I live.
The other deer was a M/L wounded one, a doe. I could have shot it again but it could barely raise its head so I stabbed it.
I have found if you approach the deer very slowly from the back they don't feel threatened as much, a quick stab is very doable.