I was interested in the Burt's Bee's product and checked that link. I see it contains titanium dioxide (which interestingly enough is the mineral rutile) as sun-protectant makeup products sometimes do. I've used similar products before. What concern me though is this statement:
This product may discolor clothing.
If it can discolor clothing, it may discolor pearls.
I love my pearls but I love my skin health more. My mother has had several skin cancers removed; I would prefer to avoid that if at all possible.
The hat is a good idea, as long as one is not where one would get a lot of reflected rays (e.g. near water.)