I will answer my own question.
I ended up buying a SanDisk extreme plus micro SDHC 16 GB (20€).
OSMC runs more than smoothly on it.
16 GB seems to be a good size. OSMC takes less than 300 MB but the ...
Naztech makes a device they call the "Xtra Drive Mini" that is something like what I am after:
It's made of aluminum, takes a microSD card, and attaches to a keyring. It has shortcomings though:
Kingston Digital USB 3.0 Super Speed Multi-Card Reader for SD/SDHC/SDXC/microSD/MS/Compact Flash CF Cards (FCR-HS4)
Manufacturer page: https://www.kingston.com/US/flash/readers/FCR-HS4
Amazon page: ...