As you know, I am not the argumentative type but I would neither anaesthetise this dog nor just leave this lump.
It looks like a simple papilloma to me, which is a non malignant growth, a little like a human wart.
Given that he is fairly amenable (and boy, have I made some mistakes over the years, presuming that!) I think that I would have a wee go at tying a nylon ligature carefully around the base of the mass, which should cut off its blood supply, causing it to fall off in about a week.
It is not a job for clumsy fingers so I would return to your vet and ask him to try. I frequently find a skilled nurse is useful as she can put her fingers through the loop of suture and pull the mass slightly away from the skin as I tighten the ligature.
If the procedure fails, little will have been lost. It is a very inexpensive technique but should never be used on wide necked growths or if there is infection or malignancy present.
Is my Vet right about anaesthetising my gundog to remove a lump