I asked this recently and someone here mentioned Blistex being safe. You can also get Dr. Bronner's although they make some kind of nutty energy bars now-but I don't know if they make them or if they just have their name on them. Rocky Mountain Sunscreen has what is supposed to be safe lip balms.
FWIW I don't think what's in chapstick is actually peanut derived. My dd doesn't want to use it though.