Off the top of my head, common sensitivities are cinnamon, clove, citrus, and mint (the last in high %). This is WRT to EOs, not FOs. FOs, go phthalate free as much as possible as it can give some people headaches.
If you're talking uber-sensitive skins, it might be better to go fragrance-free but with some botanicals or other things added to jazz it up a little. I did a beer/honey with rosemary and sage (not for pregnant women!) that was nice. I've seen goat's milk/carrot puree/honey that was pretty. And I've done cucumber and avocado puree which has a very faint scent of both and my friends with sensitive/eczema skin rave over it. You could also do a mint EO (doesn't take much) maybe with some mint tea as liquid and the tea leaves as gentle exfoliant.
Otherwise, it's trial and error.