Good call on the mask. CA is nasty, even the "low odor" version will sneak up on you. Treat it as the poison it is.
Epoxy might work if you thin it down enough to saturate but CA would be best. Go to the corner hobby shop and get a jug of the thin stuff. This is not a cheap hobby.
Staining/dying could be done if you get the outside dimensions cut and finished first and then saturate. then rough out the inside and saturate again. Slowly route until you start hitting raw wood and then repeat. In fact I'm so paranoid that I wouldn't use a router bit at all. I would find the least aggressive bit (well, not the least aggressive but you get the idea) I could find and just nibble away at it.