So, what's the theoretical harm in benzyl peroxide or tea tree oil? I used benzyl peroxide throughout pregnancy with no issues. Are you ingesting it or something?
Deodorant is fine, really, any kind of deodorant or antiperspirant is totally cool. If you are reading a site that says it's not, stop reading that site, they are giving you bad advice (for example, I recommend not getting most of your advice from Mothering.com or taking it with a giant grain of salt).
There is very little topical stuff that is going to be a problem during pregnancy and the greatest risk is usually in the first trimester, if there's any at all. I would ask your doc if you're thinking of doing something like coloring or perming your hair (although mine said it was fine and if I really was worried I should wait till the second trimester - I had my naturally curly hair permed into a different curly configuration for fun around 16 weeks).
Ask your doc if you're going to take any medicines (even over the counter) or herbs (herbs that are actually efficacious are NOT without side effects) or other supplements. The real problem in pregnancy is that very few medicines are really tested on pregnant women so the vast majority of drugs will be Category C (http://en.wikipedia.org/wiki/Pregnancy_category
) which means basically nothing. Doctors routinely prescribe Category C drugs to pregnant women if they know that many pregnant women have used it with no particular harm. Unfortunately when it comes to those things you kind of have to figure out for yourself if the benefit of taking the drug is worth a very minimal and theoretical risk to your fetus. What made me feel better is that pregnant women have been eating, drinking, and otherwise doing all kinds of things for a million years and yet our species continues, basically healthy.