I'm sorry! Anyway, I really recommend that you go ahead and get the surgery done. I'd be happy to (awkwardly) send you pictures of what my scarring looks like. But I don't think you have much to worry about with regards to it affecting your joints.
The biggest consideration people need to make about surgery with EDS is what the cause of the need for the surgery in the first place was. If your shoulder always dislocates because of a structural problem, fixing the tissue around it isn't going to fix the underlying issue and it will dislocate again. This means that you will be getting surgery over and over again.
I have had many surgeries that have gone extraordinarily well because my doctors determine whether or not I'm likely to re-injure myself. For instance, I had bilateral hip labrum tears. I took a really hard fall and my bones tore the labrum. My doctor decided that I should get the surgery done because overall, my hip stability in normal conditions would not cause this to be a problem in the future. Also, because it is made of cartilage, no amount of physical therapy would make the issue better. It was a "low risk, high reward" surgery for me.
However, I have really shallow shoulders which cause them to actually full on dislocate. I got an MRI done and I have a 360 tear in my labrum. Wow. However, my doctors warn me that getting it fixed will not actually help me in the long term - I am likely to have that injury occur again just because of the way my shoulder is structurally made. That, with the weak tissue due to EDS, makes it not worth the risk.
In your case, it seems like a "incredibly tiny risk, very high reward" situation. Your spine is probably too lax and your breasts aren't doing it any favors. You might find that it really helps you.
The things that I recommend expressing to your doctor are that 1. you need to either get internal stitches, glue, or extra stitches because your skin might behave in strange ways 2. you need to get completely put out (local doesn't always work! It doesn't on me!) 3. you might scar poorly so request that you get cut on the underside or on the side of your breast. My girl friend's doctor did it from the top (she had a similar tumor as I did), and she won't wear vnecks because of it. 4. If they give you Tramadol, which is their favorite to give because it's not as regulated as the heavier hitters, just request the phone number for the on-call doctor. You may have issues with having Tramadol work - I got a genetic test and I actually don't have receptors for it. Other EDS patients also report Tramadol doesn't work. Don't bring it up right away, though, because they might think you're a drug addict lol 5. Ask for the sticker behind your ear for nausea. I puke after getting anesthesia. Every. Damn. Time.
I hope this puts you at ease