dont know if a 38 or 357 would work or not
but I know back in the day I killed alot of whitetails with a 22 LR. From 50-100 yards. Just shoot right between the eyes and they drop instantly. Paralizes them you may need to carry a knife but they drop right there. Im sure a 357 would be plenty.
Really I see alot on tv shot with a 7 mag, 300 mag, etc and still run. I shoot all mine with a 223 or 22-250 or 30-06 in the head. I dont like having to track.