Small electric drills like the Dremel have some uses in pen repair but not that many. Mine won’t take a drill bit smaller than 1mm which is a serious failing. Also, it’s quite clumsy for precision work and the excessive speed and vibration can ruin a work-piece in an instant.
For precision work like drilling out a snapped breather tube, I use this Archimedean drill. It’s a simple spiral drill with a return spring and you can usually find it listed under jeweller’s tools. They vary a little in size though they’re intended to be worked one-handed. I use two but that’s just me – I find it keeps it steadier and reduces the possibility of accidental damage. This one takes drills up to 1.6mm, so as well as being a more precise tool it fills the gap left by the electric drill.
It’s just as easy to use as it looks, and it’s a remarkably inexpensive addition to the tool kit.