Of course, YMMV, but I would have been OK to do classes after a week. The first day or two post-surgery I felt really rundown and like I'd never feel the same again, but each day I recovered in leaps and bounds, and I don't think that's too uncommon an experience.
I had to wear a surgical binder for 3 weeks. I went out in public and to family gatherings wearing it under a button down shirt and you couldn't tell. I have pics to prove it.

I'm not in college, so maybe someone here can shed more light on what it's like to walk around campus and attend classes post-surgery, but I think you'll be fine. You wouldn't be the first one to have to get back in the saddle after only a week of recovery. I'd say if you have the chance you should spring for it. I can't say much about scars either because I had peri, but I think it's at around 6 weeks that you can be a little less cautious about stretching your scars.
Whatever you choose, good luck.