One way to skin that cat would be to attach a bluetooth serial adapter to the mini, rendering it portable/wireless, and control it over bluetooth serial from the PC side with something like Bitlash Commander: GitHub - billroy/bitlash-commander: Web-based dashboard builder for Arduino. -- which also exposes a web control panel interface so you can switch your LED on and off in the browser.
Mind the 3.3V vs. 5V supply and signal issues when you buy stuff to go with the Mini, especially if you are thinking about going with a shield for the regular Arduino form factor and some ad-hoc wiring.
Good luck with your project,
-br