Surely you mean 6.5 inches? 6.5 cm is 2.55 inches and you'd need a doctor, not a health band.
Assuming 6.5 inches you may still be a medium. The small is really quite small. I went to a MS store to try them on because I was concerned with my skinny wrists (which are actually 7.5" around). I was surprised to find I was a medium and even then not using the tightest setting. You'll likely be a medium, but you should try one on if at all possible.
Check out reddit too , as this was discussed there. /r/MicrosoftBand/
Is the screen size the same, regardless of the Band size? Example, my wife is wearing a medium and she has it as tight as it will go, but it is still a bit too big. If she gets a size small Band, is the screen going to be just as big on her wrist?
The only difference between the sizes is the "height" between the back of the display and the heart rate sensor. The display itself is the same for all sizes. For smaller wrists, I fully expect to see a gap on the sides of the wrist between the skin and the inside of the band. As long as the two metal sensors are in firm contact, it's the right size.
My wrist measures just over 6.5" and I have a Large Band. It gives me a good working range of where to wear the Band. Also, I don't like having tightly fitted watch so the Band fits loosely where it can move up and down couple of inches on my wrist.
I tried Medium at the store and that would work but felt bit tight so opted for Large.