Você não precisa copiar sua chave ssh se não gostar, Você pode encaminhar a sua local com -A
-A Enables forwarding of the authentication agent connection. This can also be specified on a per-host basis in a configuration file.
Agent forwarding should be enabled with caution. Users with the ability to bypass file permissions on the remote host (for the agent's UNIX-domain socket) can access the local agent through
the forwarded connection. An attacker cannot obtain key material from the agent, however they can perform operations on the keys that enable them to authenticate using the identities loaded
into the agent.
Eu uso assim,
ssh -At user@server
ou em algum momento, até eu tenho que pegar outro host, então eu posso rodá-lo assim,
ssh -At user@server -- ssh -At user2@server2