Live linux with no HDD has the obvious issue that you can NEVER reboot the computer or allow a power failure to happen, until you have fully verified you have the keys correctly on some other media.
Instead, as I suggested, having it temporarily on a HDD, in a password encrypted wallet, allows you to safely decide when you no longer need the computer wallet.
Live OS can have persistent storage too, so it's not that different from a hard drive. Also, OP is talking about cold wallets, so there's some time between the creation of the wallet and the first incoming transaction, so sudden power failure is unlikely to cause big problems - the only risk here is some complete noob just forgets to backup the wallet.
Who knows what backdoors and security vulnerabilities every motherboard in every computer might have?
So you shouldn't use any computer?
Printers are connected to the Internet these days, and they are much less commonly audited than motherboards or CPUs.
Perhaps just unnecessary paranoia but there is a way to mitigate this. Some pretty cheap printers has no capabilities to connect to the internet and would thus not be able to transmit any information other than through the cable. Printers do store cache so I imagine that'll be an issue. If you really are that paranoid, you can destroy the printer after use/use it exclusively for paper wallets.
Or just use a mnemonic seed and write it down on paper, or use some of those steel plate solutions if you're really paranoid.