If you don't trust the computer then your best option is a hardware token like the Trezor (which already supports WebAuthn in addition to its cryptocurrency fun

If you don't trust the computer then your best option is a hardware token like the Trezor (which already supports WebAuthn in addition to its cryptocurrency functions). The better ones will include a screen where you can see details like which site you're signing into before confirming the request. Either way, the host computer never gets access to any private keys. It can still do whatever it wants with your login session on that site, though, so you'll want to be careful about logging in to sensitive sites from untrusted PCs. The same applies to password-based logins, of course; moreover, any password you've entered into a public PC should immediately be considered compromised and changed (from a secure device) at the earliest opportunity. Given any choice in the matter I would suggest using your own equipment to change the flight (e.g. a smartphone), even if it's less convenient.