Copy ssh key or create a new one

I agree with https://unix.stackexchange.com/questions/208495/ssh-key-authentication-with-multiple-computers. You can do any one, but each one has its pros and cons.

I would prefer to create a new SSH private key for every trusted machine. That way, if one is compromised only the key for that machine needs replacing. Copying private keys around could also increase the chance of somebody else getting access to it. It basically becomes a single point of failure. There is a reason why sites like BitBucket recommend their users to replace their SSH keys every year.

As long as your private key is secured using a good quality pass phrase it is safe to copy it from one machine to another.