Admittedly, it's a short list given that traditionally, the majority of martial arts focuses on sparring and competitions. But here are some to try:
Boabom (of course!) - originating from ancient Tibet, Boabom has a few variations so you can try out and study the one that's right for you. There's Seamm-Jasani, otherwise known as gentle Boabom, which uses slower movements. Osseous Boabom is more energetic and incorporates more self-defense moves. There's also Yannbao, which is Boabom with the use of staffs that act as an extension of the body. Each variation has its own style but all are no-contact, non-competitive martial arts.
Tai Chi - Tai Chi is a self-study martial art that won't require you to make contact with another student and yet has been known to deliver self-defense moves that can be used when faced with a confrontation. The only thing to keep in mind is that today's version of Tai Chi has been watered down compared to when it was practiced in China before the 20th century. However, it can help improve your strength and coordination and manage stress.
Iaido - this is a Japanese martial art that focuses on swordwork and teaches you how to quickly draw your sword in response to a threat. There's no contact or blade clashing, but it will help you develop physical strength and reaction skills. An Iaido class can be surprisingly intense and work your core muscles.