You are probably stuck with having to do this manually, if you don't want to compromise security.
One other poor choice - write a
daemon - one that runs as root. Write the temp script to a protected directory via scp. Have the
daemon run the script when it sees it out there, delete it, then email the output to you.
Can you push back on the limitations - like no crontab? You can always explain to mgt that you may be out days when this has to run. The reason I say this - it sounds like an arbitrary decision somewhere upstream.