If you are prepared to let them run ssh using sudo or by setting the suid bit then why not just give them the key? You won't be letting them do anything they couldn't through the other methods.

ssh -l userX machine

You will also need to consider security, I would set up an account for this single purpose, write a script with menu options for the permitted functions. Ensure that no command gives a command shell or that control-C doesn't drop you there. Set that script as the shell in /etc/passwd.

sshd will also have to be configured to only permit the script. Look for ForceCommand in the ssh docs