Honestly if I lived closer to the city I’d probably go looking for a Tai Chi group. That’s about as close as I can get.
Also considering fencing when I lose more weight/am not the world’s largest target. There’s options, but they deviate pretty heavily from the road I’ve been on in life thus far to the point I’ve only recently had them become plausible.
Whether or not you'll be able to progress in belts/ranks is different but who cares. Wearing a white belt forever is probably better for character development. If your goal is the belt just go to the store and buy a belt.
There's also archery and I'm sure there are many other options for no-contact martial arts training. If fencing works for you then there's also Kendo. There's Iai-do which is just about drawing the sword. Lots of options in theory.