We have the 'death barrow' ie a wheelbarrow which we put any corpse in and cover it thoroughly so passing folk can't see what's in there - nor me. We put it at the gate, so the knackerman can collect it without us being there. Ours are very good at coming that day or the next. Obviously it will be more difficult to leave the body out for several days, but if someone tries to steal the barrow they will have a nasty shock. The barrow has to be disinfected after the collection, handles as well, as knackermen are not reknowned for washing their hands between collections.
In order to do as many collections per day as possible and keep waiting times short for everyone, the knackerman will not be able to hang around to try to find you if you are working outside, so it's best to have the body somewhere readily visible and easy for him to collect.
It may sound hard, but once your favourite sheep is dead, it's just another sheep corpse, sad though that may be.