Hey, Emily!
I'll be 4 weeks post-op on Tuesday, so it looks like we're right around the same spot. I was only completely banded shut the first week after my surgery and now I'm allowed to take the rubber bands off 3 times a day to eat soft foods. I see my surgeon at least once a week just to make sure everything's going all right and I remember asking him one or two appointments ago if I was allowed to use a straw. He said yes, provided I don't stick the straw between my upper and lower teeth. Basically, as long as I just stick the straw in my mouth in front of my teeth, I'm good to go. (Since you're banded shut, that won't even be an issue for you.)
Most of my stitches are not dissolvable, so the incisions in my mouth still hurt a little when I smile too wide or when I suck too hard on a straw, so I really don't use them too often. I had a milkshake a few days ago through a straw and, of course, that required more effort and a little more discomfort than just drinking Coke through a straw. It's a little bit of an adventure trying to find a good technique, but once you get it, it really can be much more convenient.
You probably want to double check with your surgeon, though, before you do anything. I would hate to think that my advice ended up causing you and trouble or pain. Good luck!
Becky