if you actually want the entire braze-on off, and have a propane torch, go with a torch.
if you have very steady hands and are patient you could probably do it with a dremel.
if it were me, i'd probably use the dremel and take off most of the braze on and just leave the base so i don't risk cutting into the tube. or you could use a dremel for most of it and take the base off with a file. you'd be surprised how well a properly used file works. just take your time and check the progress after every stroke or two.

now that i think about it, the dremel/file solution would probably do the least damage to the paint. so i'd do that.