I haven't had to do a lot of brace carving through the soundhole but I've had to make some adjustments that way.
Out of my arsenal of tools the standout for that job ended up being a couple of the Ibex arched sole finger planes violin makers use.
Though you are not trying to get a concave carve with the arched sole the arch helps take small amounts of wood and they are easier to push accurately.
They are not much bigger than your finger so are pretty easy to control in limited space. Once carved, a little sanding and they look pretty good again. The planes being "finger like" they are easy to get used to using them blind.
International Violin has a great selection and some knock-offs that are very reasonable. I do love the little Ibex planes though, and they are ready to go out of the box.
https://www.internationalviolin.com/tools/planes/?per_page=48&sort_by=1