Honestly, it would do you good to address this fear. Drains are a very real possibility regardless of whether the procedure uses them or not. I did have drains post surgery and you won't see them, know why? You have bandages or a compression vest while they're in and you shouldn't really remove that until after drains are out. You're also numb in that whole area so you don't feel it. In my opinion it's not really worth going above and beyond to avoid drains because guess what? I had to get another one because of post surgical complications. That's not a regular thing but it can happen. It's also a reason I'm currently eternally grateful I stayed local because I had all the support post surgery (most hospitals and surgeons won't touch another surgeon's work) but that's another story.
It's better to address the fear than to find a way around it because things can go wrong and if you can't get a handle on that fear now, it's going to be worse if you're down and have to face it. The drains are really not a big deal in the slightest. I've dealt with chest drains in the past and they're horrendous. I was worried it would be a repeat of that but it was a necessary evil and in the end it was a lot of worrying for nothing.
As for pulling them out, don't worry about that happening. They tie them in there, it's not loose, the sutures are wrapped tight around the tube and the same suture is tied into your skin. It's a very strong hold. After DI, you would struggle to have the strength to yank them out and they're not coming out accidentally. You're not going to be doing anything remotely strenuous enough for that to be an issue during initial recovery. I have one in right now and I'm going to and from work on public transport during peak times, and assisting in Taekwon-do classes (not taking part with drain in, but still showing movements slowly) and although I feel it more because I'm not as numb, it's more an awareness than any hint of pain and never come remotely close to yanking on it or anything bad happening.