its do - able but I wouldnt. Not my cup of tea at all. Its either going to be an execution or a wounded runner.
You will need a decent quality pistol though - such as a Wierauch HW (but watch out as the target based Hws only put out about 2.5 FPE) or a Brockcock Aim X. Avoid Co2 pistols at all costs - mostly have crap triggers & are very temperature sensitive.
You will need to keep it in a case (that renders it impossible to fire) when you are not on land that you have consent to shoot over.
Plus get a load of practice shooting it before you contemplate trying to dispatch live quarry - its suprisingly hard to shoot accurately with a pistol - bearing in mind you only have a kill zone the size of a walnut (between the eye and ear). You will probably need a scope or red dot sight - iron sights are also difficult to get consistent accuracy with.