How can I get my Steam Cloud saves without installing the game?

This should now be possible through https://help.steampowered.com/en/accountdata thanks to GDPR, at least in part. Specifically the Steam Cloud link under the section "Uploaded Data".

You can download the files one at a time from here: https://store.steampowered.com/account/remotestorage

Or you could just download the game, synchronize it and then move the files.