Using any sort of hardware security module, such as a smartcard (which some YubiKey devices can operate as) will not allow your private key to be compromised be

Using any sort of hardware security module, such as a smartcard (which some YubiKey devices can operate as) will not allow your private key to be compromised because you have no access to your private key -- it's on a whole separate computer (the HSM) and your only access to it is by sending APDUs to that computer. For a typical smartcard the only thing you can ask it to do with your private key is to perform cryptographic operations on data with it. Many smartcard applets require that you authenticate yourself to the smartcard before they will even do that. I use a smartcard with a NIST SP 800-73 applet on it for all my SSH (and TLS) sessions and do not have any other SSH keys.