Yoou could try a piece of moleskin on the inside of the strap, this is what we use for blisters on the heal. It should work.
If you only wear them occasionally try what's called "body and clothing tape" or "fashion tape". It's a double sided tape that won't hurt you or your clothing. Models, etc. use it to hold up dress tops or hold down swimsuit edges. You can find it at most fabric stores either with sewing adhesives (like stitch witchery) or with undergarment supplies (like hooks and eyes or bra extenders).
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