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@hellomiakoda Not a stupid question at all; it's a common enough challenge to overcome.
I've been known to pull the following old-sysadmin dirty hack:

• 0n the workstation that's already set up, open ssh sessions to the server and the new machine respectively
• cat the private key on the new machine
• Open ~/.ssh/authorized_keys on the server in a text editor
• Copy-paste from one terminal to the other, using swipe-and-middle click (method may vary between distributions).
• Save that file.
• Test that you can connect from the new machine, and adjust/edit as necessary.
• Once you know it's working, clear or exit the terminal on the new machine.

Of course, this assumes the new machine has ssh running and that it accepts the key from your first workstation.

Failing that, Manu's sneakernet solution is pretty reliable.