I have been making a rather lovely lip balm with Rosa Rubiginosa oil, Hazelnut oil, Cocoa Butter, Beeswax and EOs to taste.
However, after giving out a number of samples to friends, I realized it would be a bad idea for nut-sensitive people to use this.
Does anyone have any oil preferences for lip balm that they can recommend?

I make my own lip balm too. My lip skin becomes too dry and cracked constantly so I make something thick and heavy. What I use is Cocoa and Shea Butters, Unfractionated Coconut Oil, Sweet Almond, Argan, Pomegranate and Rosehip Oils and a small amount of the Cacao CO2, which is absolutely lovely. You can avoid Almond and Coconut oils, but all the rest are particularly great, nourishing and repairing for lips, even without Almond and Coconut, and I've never heard about the rest being bad for people with nut allergies, but if you know, tell me because I give samples to my friends and family too! Also, Argan, Pomegranate and Rosehip are highly antioxidant and everything tastes amazing too!

Argan and Pomegranate sound wonderful!
I haven't had anyone complain about allergies to products, yet, but I do know several people who have severe nut allergies, so I would rather steer clear altogether, if possible.
Do you combine the Shea and Cocoa butters or use them separately? I have heard that Shea can be grainy unless it is melted at a specific temperature.