There are two types of culling.
The first, and what most are talking about, is sending off ewes as 'cull ewes', i.e fattening them and selling them at market into the food trade. Culls are making very good money these days, so its a decent option as long as the animal is sound enough to walk etc.
The other, is having animals put down, your options, depending on how you feel, are the vet, the knacker man, or yourself. A .410, a .22 (either pistols or long arms) will do the job adequately.
I also totally agree with Fleecewife. It is fairly silly to be taking in, animals that you know stand very little chance, you are only bringing all manner of bugs onto your farm and ultimately causing the animal extra pain and suffering, because you want to save it. Part of good stockman ship, is knowing when enough is enough.