This a great idea.
Please show us timid ones a bit more on how you did it. Dimensions. Possible problems to avoid.
Take the case apart and you will see that the thumbwheel assembly actually has an extension lobe that goes to the left. You can see it in my photo above through the shrink tubing "button", it's the grey you see. The extension lobe is over the actual select button and thus pushing the thumbwheel also is a push on this extension lobe and causes the button underneath to be pushed. But since the button is far from the wheel over doing it when pushing the wheel is possible and there are thin supports for the wheel that tend to break. It really is a poor design.
Anyway, the idea is to just directly push down right over that lobe, so just eyeball where that lobe is under the cover and drill a hole the size of whatever your button is going to be and insert the button in.
Avoid any of the strengthening ribs molded on the back of the cover when drilling.
I plan to epoxy a thin sheet of styrene on the back of my button, larger than the hole, to keep it from sliding out the front which happens occasionally. Has to be thin enough to not activate the button though, which shouldn't be a problem to accomplish. Again, there is probably a way better solution than the shrink tube which is all I could find at my fingertips at the time 😂, like some off the shelf plastic button or something, or piece of an old TV remote rubber button thingy, but I can find. A dowel would work too as pointed out above.
Another point I feel like I want to make is that I also bought a new remote and will put a button on at some point but I have learned that you don't need to push the wheel hard at all to select (at least when new) . Pushing lightly should save those thin support arms There is a bit of a delay for the selection to show and I think that delay causes users to push hard thinking that the push didn't work.