Should injured/infected tail of a 7 mo old cat be amputated? How long should we give it to heal befor deciding

Adopted stray cat with injured/infected tail at very tip. Vet treating w/Amoxicillin, but suggested amputating entire tail. Plan to keep him as "indoor only" pet with 3 other adopted strays.We are worried about it being painfull and tramatic. Comment please.