Just from a general security standpoint, you wouldn’t want to copy/share private keys. The proper way would be for each device (or at least each user) to generate its own private/public key pair, then push the public key to each server. That way, if an iOS device is stolen, you just remove the public key from the server, and also if a new server is brought online, you just clone the authorized keys.
If you want to manage by passwords, then what @JKoopmans suggests also works. Data Jar is a great way to store information outside of the shortcut. Still not the most secure, but definitely better than embedding in the shortcut.
Based on the use case you’re suggesting, I’d recommend going the key route since it sounds like you’re executing basic commands or triggering scripts on these servers. Passwords make more sense for full on terminal interaction