I would not advise cutting up perfectly good sized fabric into smaller increments. I agree scraps will come from other projects too quickly!
Try participating in a number of swaps on this Board and on the other internet sites to get a variety of charms you want to collect.
A few months ago I hosted a 2 1/2" strip swap the width of the fabric on the Board. Hang on for that to begin again soon.
I've participated in Nickel and Dime and Candy Bar charm swaps and most recently a 1 1/2" charm swap.