I'm confident about vegetable oils. A few ones are known to react with air, but sunflower and peanut oils are rather unreactive, and the watch is closed. I used some in lieu of thermal grease at a processor, at heat for years, an it didn't smell. Just experiment, if these oils don't fit, you can still replace them with a more expensive silicone oil.
I ignore dyes very accurately, so hopefully someone else answers.