Mouse,
I have to admit I've never tried to install Linux on a memory stick/thumb drive, although I have experience installing Scientific Linux in a VM on my Windows 7 computer.
"To first approximation", there shouldn't be anything special: it's just a small disk that's happens to be connected to your computer by USB.
Searching Web... Here's a preliminary discussion about installing Mint on a 32GB stick:
https://forums.linuxmint.com/viewtopic.php?t=205310
It looks like the novice in that thread just stopped asking questions, although the expert who was trying to help had done it many times.
AHA! Here's a silent video created earlier this year showing how to do it. Instructions appear in a text window. Its author recommends using a 32GB stick, though.
https://www.youtube.com/watch?v=6NHWpi7cQxQ
He's running from a Live Mint USB stick, creating a full Mint USB stick on a computer that has Windows on an internal hard drive. That sounds familiar![]()