Is there anything I can do about ghosts and tombstones that's safe for my game?

I usually just let the graves stay on the lot. Adds some unpredictability to the game with the haunting.

Yes, this means that Sims with low hunger at night really have to avoid ghosts or risk being scared to death, but that's something I enjoy - making the game more challenging.

Ghosts can't cross water so if you don't want to make a cemetery for them, you can just put a mote around them and the ghosts won't be able to haunt around your Sims.