I love rotary tools for their ability to cut quickly... hate them for the dust. A nice compromise is an oscillating tool - a lot like what the doc used to cut your cast off your broken arm. Easy to control, doesn't sling dust everywhere, cuts nicely (not as fast as a rotary, of course). If you do happen to bump against it, it most likely will NOT cut you (or it will very slight).
Once you get it out, which is really pretty easy, and prep the area, then you can decide if you want to glass a new piece of wood in place or whatever. PVC, as stated, would be simple.