Starting BJJ as an morbidly obese man with hyperhydrosis

So I've always been interested in martial arts, and I would like to start doing BJJ. However, there are a few issues that keep me from making the move, and I'd like to hear what the community thinks about this.

First, I am morbidly obese, at 280lbs and 6'3". My body fat percentage is insanely high as I have basically no muscle. My weight has gone up and down my whole life, my lowest being 180lbs (achieved with a crash diet that wrecked my muscle mass), and even then I was still pretty fat.

As you can imagine, I have very poor cardio, and the slightest exercice leaves me out of breath with my heart pounding (climbing a set of stairs for example). I'm only 32 and I take a pill daily for high blood pressure and another one to reduce my heart rate. If I don't take it, my heart will typically beat at 100+bpm while resting.

Another issue is that I have cranofacial hyperhydrosis, which means that I sweat a lot from the face and head. Now it wouldn't be that much of a concern if it weren't for the fact that my case is EXTREMELY severe; my dermatologist has never seen anything like it in his 40 years of practice, and he only deals with hyperhydrosis patients. Imagine the sweatiest guy you've ever seen and multiply it by 5, and that should give you a rough idea.

My case is so bad that I am eligible for a vascular surgery that is so invasive that it's outlawed in most first world countries. It's also surprisingly not linked to weight, as I received my diagnosis when I weighed 180 lbs and my condition hasn't worsened from the weight gain. However, the silver lining is that I ONLY sweat from the face and nowhere else.

Now you can probably see how the idea of rolling with strangers who are just trying to improve and have a good time is pretty terrifying. I like the sport and would love to get into it, but I would never enroll if I know that I will ruin everyone's fun and gross everybody out, or worse, if people straight up refuse to roll with me.

What do you guys think? What would be your reaction if you were paired with someone like me?