How do I make a clickable shortcut to open a random shortcut file in a dir on Linux?

I have made a directory on my Linux Mint desktop called "Ungoogled Chromium shortcuts". It contains one .desktop file per proxy I have access to. If I open this directory and double-click one of the shortcuts in there, it opens Ungoogle Chromium with the correct --proxy setting. Now I'm trying to make it so that, instead of manually opening the directory and picking one of the shortcuts, I can just click a shortcut directly on the desktop to open one of those shortcuts at random. How would I accomplish this? (Without installing any extra software.)