I don't think you can get a .375 conical to fit down a .36 caliber barrel. Those are made for the .36 cal. pistols, which are larger in bore diameter than the rifle.
Try using a standard .38( .358") Caliber Wad cutter, in that .36 rifle for a " conical. Keep the bullet length short, and the weight down. Use an OP wad between the powder and the bullet to protect the bullet from gas cutting.
DO Check your hunting Regulations to make sure such a small caliber rifle is LEGAL to use on deer in that jurisdiction. Even if such a caliber is " legal", It would not be my first choice for a deer gun, even using conicals. Most .36 barrels are designed with deep grooves, and a slow twist barrel- usually 1:48" That is too slow to stabilize anything but short bullets, and then only if they are screaming out the barrel.
I am assuming that one of the reasons you have chosen that caliber for this handicap shooter is to limit the amount of recoil he is going to feel when he shoots it. Well, if you start shooting bullets out of that barrel, at speeds approaching 2,000 fps., he is going to feel RECOIL. The standard lead round ball in these caliber guns weighs only 60-65 grains- and is the reason you don't feel any recoil- even at 2,000 fps. A .38 wadcutter will weigh 140-148 grains. There are lighter .38 caliber bullets, for sure( Lyman Cast Bullet book shows older molds for as light as 90 grain bullets; I have shot 130 grain bullets in that caliber), but how good they will be for shooting a deer sized animal is another issue. :thumbsup: