This thing seems fishy to me. If you want something that is mostly under your control to which you can install open source stuff into then buy some smart cards and card readers e.g. from https://www.javacardsdk.com
Carrying your own smart cards and smart card reader may work for some use cases but I'm sure you can see why a small key attached to your key chain is a better solution in most cases.
There are readers the size of a thumb drive, cards themselves are the standard credit card size or even SIM card size if not contactless. It's not the real issue here, there are a few more important ones such as lack of desktop browser support for U2F NFC use case. U2F applet works fine for me on Android though.