Rhys, at barn and yard ranges - 10-20 yards - wadcutters, hollowpoints and Polymags (assuming you hit the spot) will all deliver a clean kill. They are all more than capable of going through-and-through at close range, especially in .177 and while they may make more noise on impact, your quarry is no more dead - remember, sound energy is wasted energy.
I've tried them all and always come back to a quality roundnose brand. Hobby, for example, can be highly effective, but don't ride the breeze very well and exotics such as Polymag are very expensive, while being no more effective than a domed design.
The only real way to reduce the risk of overpenetration is to reduce the ME of the rifle. I use a 7 ft/lb HW30s for such work and even this can go all the way through on occasion.