Back when Remington made the bolt action XP-100 pistol, one of the rounds they chambered was 35 Remington. I bought one of those guns used, put a 4X Leupold pistol scope on it and went to handloading. I had read in an gun magazine that some of the hand cannons were as accurate or more accurate than the average factory rifle. I didn't believe the article, but quickly found out that it was true. With a 150 grain bullet, I soon had a load that would put 3 shots in 1/2 inch at 100 yards off of sandbags. But, with the short barrels, even if a pistol is very accurate, you will be limited in range compared to shooting a rifle.
I never took it hunting, but it would have been an excellent deer round for a handgun. I've kicked myself 100 times for selling the gun - not because I needed it, but because it was such a novelty, and I didn't have a lot tied up in it.
Thompson has made a lot of different big bore calibers for their Contender Pistols, and I've been told that they are very accurate as well. If I were serious about buying a pistol to deer hunt with, that is what I would check in to.
Right now I sometimes carry my 357 mag Smith revolver and wouldn't be afraid to take a 40 yard shot with it, but it wouldn't compare to a nice Contender or XP 100.