I did this a few years ago when I had to remove a DIP and a five-lead TO-cased
buffer from the top of a board.

The TO package came lose with a pair of cutters. I don't remember how I
removed the DIP, but I'm pretty certain I used a cutoff disk. (Even if you
have fine-tipped cutters, you run the risk of damaging the board from the
force exerted.) I don't remember what I did about the fine shavings (if there
were any).