Antiperspirants and deodorants contain the same ingredients for both men and women, the difference is in the fragrance. If you don't mind smelling like a pine tree, then swipe away.
As for his used razor, it's generally better to use your own because a dull razor can cause nicks. In a pinch, go ahead and borrow his razor, it's not going to give you a disease (sorry Cousin Cat).
Other things to consider about his products: women's shaving creams tend to be heavier, but there's no reason not to use a guy's cheaper shaving cream to shave your legs. As for cleansers formulated for him? These are OK for you, but many are created to prepare skin for shaving and these ingredients could dry out your skin.
Now should you use his toothbrush in a pinch? Well, I'll leave that decision up to you. You do kiss the guy, after all.
