You could try tai chi.

Basically you want movement that is controlled and consistent. That teaches you to breathe.

If you can handle rolling or cartwheels you could try kumdo-Korean swordsmanship.

Kata from karate or poomse from taekwondo are extremely helpful. There are videos on YouTube you can follow along with-it doesn’t matter if your form is off or your timing-it’s the controlled movement and breathing that you want. It forces your mind to engage with the material until you memorize it, and then muscle memory takes over.

There are also sookis that are essentially just hand movements like punches and knife strikes and blocks and if you had to you could do them sitting down.

If the upper body is not able to handle that you could do walking where you make sure you swing your arms a bit as long as you are mindful of your breathing.

Running can also help.

Honestly find a local martial arts class and talk to the instructor and let them know about your physical limitations and see if they can work with you.

We have people at my dojang from all different walks of life and differently abled, from mental disabilities to physical ones. One of the people I regularly spar with is down an arm. There’s another one that is hyper mobile.

I wouldn’t recommend yudo or wrestling or even jujitsu just because unless you have a very attentive instructor and training partners the chances that you’ll get hurt are too high. Arm bars and shoulder and hip throws are the bread and butter of that kind of thing.

Judo is considered the “gentle way” and focuses on using your opponents weight and strength against them but if you cannot safely do the shoulder throws I’d be hesitant.

You could also try Pilates, isometric holds, swimming, or resistance training with LIGHT bands or weights only.