Camellia flower oil. My dad gave it to me, and nothing has happened to my bat after two seasons.
Camelia oil is used more as a rust prevention measure on your tools
Might give Danish oil and Tung oil a go.
Walnut oil might do a job, but will darken your bat.
Olive oil will go rancid after a while and make your bat smelly.
Mineral oil (aka paraffin) could work and probably won't change the colour.
Lemon or Orange oil will also work, and give your bat a nice odour, however orange will stain your bat. I don't think they will go rancid either.
Don't use chilli oil, it will melt your grip and stickers (don't ask how I know...)