A lot of people teach in multiple worlds now. I use Fitness and Wellness, and am covered for both yoga and fitness. I think the best thing is to call your company (or the company you are thinking of using) and ask for a quote based on exactly what services you plan to offer.
My guess is that things like karate and other martial arts that use weapons and do sparring with physical contact would be more likely to carry a higher cost than something like tai chi, but it is certainly something to ask your insurer.
if you look at the quotes you get on this website, you’ll see that they all talk about “less than 50 cent a day” regardless of whether you look for coverage for martial arts, fitness, yoga or Pilates which indicates to me that the premium will be same for all of those disciplines from The Fitness & Wellness Insurance that is associated with IDEA.
Are you a certified instructor? If you are, many certifying organizations have agreements with liability insurance providers to cover their members at discounted rates. Some providers do and some don’t require certification of some type. If you are an IDEA member, IDEA provides access to it’s members to such insurance.