Low velocity rounds need a little expansion for shock effect in small caliber handguns. Faster rounds do much better.
I shot around 6 deer with 180 gr. .40s (different companies). Took 3-4 shots (all in vital areas) to put them down. The 165 Sierras showed expansion, almost always complete penetration, and signs of shock effect in the meat.
Getting a 180 or 200 gr. bullet in a .40 Short&Weak is a little hard on the gun.
I've witnessed 4 deer taken with 38 gr. HPs, subsonics, in a handgun. All dropped instantly.
Bullets effects on any game depends more on shot placement rather than size of the gun, size of the bullet, or velocity, USUALLY, but on deer size and less velocity helps a great deal.