Every country has different cultural greetings. I was wondering if handshaking is ok in Japan? Or do they have their own cultural greeting. I'm not talking about greeting in their language but more the body language.
As long as you are polite for western standards it is usually fine.
Handshake is OK although not common among Japanese people. Some Japanese businessman go ahead with handshakes when greeting foreigners, though. Hugs, kisses and other close contact, must be avoided and never ever tried.
Slight bow while shaking hands would be just perfect.
Japan is pretty well-known throughout the world for its bowing culture. If you are in a semi-crowded place, you are almost guaranteed to see numerous people bowing at each other as they greet or say goodbye, so just mimic them. A slight bow works - I would recommend ignoring any articles on the internet that over-stress the complexity or the importance of the angle/degree of bowing unless perhaps you are greeting someone of extremely high importance. The truth is bowing is really easy once you see a few other people do it.
Japanese people are well-aware that many other cultures greet by handshake, and some people will thus be eager to use a handshake with non-Japanese people.
Either way works.
From my experience the best way for a tourist is to wave a hand and say "Hello".
Many Japanese are interested in practicing their english so it may be a good and easy way to start a conversation with a stranger.
For "westernized" Japanese, business or being introduced to a Japanese by a friend (including women) a handshake is ok and no more.