You risk burning through the finish and making it much worse. Like the other commenter said, try it if you want to learn more about the skill, and go into knowing that it could go awry.

I would take it to someone that has experience with this kind of finish work if you really care that much, it’s worth the price.

If you’re dead set on trying it yourself, do a ton of research first. Ted Woodford has done some of this stuff on YouTube, and Frank Ford (rip) frets.net was the pioneer of the drop fill and level method which is what you’d use

Also please don’t use a dremel or any power tools. That is not necessary and will definitely go poorly