Vet knows best? Surely not!
I have cut off a few of these, they bleed like stink, tbh I don't use cautery as either you leave unhealthy tissue or you burn healthy tissue, I cut it and the wall around the root away and put a serious pressure bandage on the stump of the strawberry. Generally I give a bandage change after a few days and generally it works first time. The growth is not well innervated, just tip, nip and bandage hard while getting covered in blood (bigger growth bigger blood supply) you could give a sedative if the farmer was unable to hold sheepy still.