To use your hanko in a situation like that, you need to register your hanko with the government. Some Kanji characters have masculine meanings, and some have feminine meanings. So, if we know the gender of the user of a hanko, we will choose the characters accordingly. But there are also many characters of which meanings are neutral. Koin-tai is the most common font.
Organizations tend to use other fonts.
But they are very difficult to read even for people in Japan. So, if you would like to make your hanko readable, choose Koin-tai. It's the most commonly used kind of wood for hanko. 3 different kinds of font are available. Click here to order.