I think Eric at On Scene Tactical used to make a kydex sheath that would hold Chapstick. I can't imagine it would be too difficult to make it work for a tube of Bert's Bees.
You could also check out some of the sheaths with an elastic loop on the side for a flashlight- I'll bet that could also hold a small tube.
Those would be the thoughts I would have off the top of my head for a ready made product, assuming you weren't thinking about something custom made.
Def