Hornady 200 gain RN needs a minimum of 1600 fps for complete expansion. This bullet is probably not a good choice for use at handgun velocities - unless we are talking about 50 yards or less. The single shot pistol bullets are designed for just that - single shot pistols. The varmit bullets offered by most manufactures' are also used in single shot handguns with stellar success, (Hornady .284 V-max). Why?, because of design.
Lone Star, I don't quite understand your statement about handgun bullets being too soft for deer (thin skinned game)? The velocities that are generated by the 35 Remington in handgun trim are not that fast, I've been able to push a 200 grain to 1900fps, and I don't consider that fast at all. What you are saying that a 120 grain single shot bullet skipping along at 2300 fps+ is too soft for medium size game? Hope knowbody tells my 7-30 Waters that..........
Call any bullet manufacturer, tell them the velocities the 35 Remington is producing (either muzzle or beyond), and see which bullet they lead you to.
That doesn't even bring into account the twist rate that most T/C barrels have in the 35 Remington - anything under 180 grains is probably a gamble as far as accuracy is concerned.