Doesn’t sound like Clonezilla would be a great option then. The keyboard is necessary for that as it will be how you navigate menus and input your clone image name.

You can use the Steam Link App from a laptop to help manage desktop work, assuming there’s one available to you. It would allow you to have a keyboard to use on it remotely.

What I think you’ll really want to do is to grab a copy of your user’s home folder, which IIRC will also have all your Steam Library games. Once you get your external drive, this should be easy enough.