My surgeon said that he would not remove the skin tags, because they would just grow back.
However, I ended up having surgery for a perianal fistula, and right before I went under I said "Hey, while your down there, can you chop those off?" He did. They grew back.
Since I have been in remission though, they have disappeared.
I can't really say how painful the recovery was for those, because the surgery sliced through my anus - but THAT was very painful!