Japanese incense is often made from food-grade powdered organic (as opposed to inorganic) ingredients and as such often doesn't trigger scent-related reactions. I found this out when I was first introduced to a line of Japanese incense after years of wanting to vomit around bamboo-dipped stick incense sold in head shops, kitschy boutiques, and on street corners. You might find it really doesn't bother you that much.

As for wearing a face mask, it's typical in Japan. No one with question you about it. You'll fit right in around the bigger cities.