When I got back, I got to looking for a USB SD reader to keep on my keyring. There were several choices that called themselves "keyrings" but they didn't have a loop on them or the loop was on the removable top (don't get me started on that!).
I finally found the I-Rock IR8200 at Newegg.com for $12.99 and $4.99 shipping. Here's what it looks like:
You can't tell from this picture but mentioned in one of the comments was that there was a loop on the swivel cover for the USB plug. I could use that to put it on my keyring.
So I ordered one and it came in today.
It's larger than I hoped (but honestly not larger than I expected). Here's how it compares to my Sandisk Micro USB drive and an SD card: