The .handgun will be good for finishing them off at close range, but little more. For youe 20 ga. get some number 4 Buck shot, not number 4 shot. If your gun is a 3in. gun get 3 in. shells. With these you should be able to hit them hard enought at 60 to 70 yrds. to at least get off another shot. I would recomand that you eather buy or borrow a centerfire rifle in .223 cal. or larger. With a good hit from a rifle you`ll be able to kill them as far out as you can hit them. Depending on the cal. and if the gun is scoped, from 100 yrds. to 500 yrds. You can pick up a NEF single shot rifle for under $ 200 without a scope. If your any kind of a shot it should be good to at least 100 yrds. If you put on a good scope you should be good to 300 yrds. with a rest to shoot from.