This idea is based on a toy doll and a rubber coated thumb drive, and the technical skill of sewing.
I had might not thought of this if it wasn't for the rubber coating, so if you can not find a thumb drive of this kind, you might have to experiment with glue. I tried once with a regular thumb drive, and attach an elastic band to the doll to fold around the thumb drive, sort of like a mitten. That turned out to be too difficult for me, but also an idea if you like.
So, here is the list of what you need:
1 toy doll of your preferences (i found these $0.90 ones at IKEA)
1 rubber coated USB thumb drive (this one works perfect)
1 sewing thread of perfect color
1 sewing needle
1 pair of tweezers
1 tiny sharp knife thingie, called seam ripper or stitch ripper