my two cents, if I were the admin there, I would insist on WSUS just like everything else. Having one-off methods of doing things due to no real reason other than they don't want to do it (not you, but the "admin") would be a sure-fire way to be shown the door and out I go...
doing a group policy for WSUS is pretty easy... that's what I'd recommend. I have then used lansweeper in the past to verify the WSUS registry settings for the machines (if you key off of the registry keys)
you can use group policy or registry keys to tell the machines to go right out to Microsoft, bypass WSUS, and just patch and reboot/etc, but I just can't bring myself to link the steps 🙂