Victorinox or Wenger Soldier is a military issued model that was made from 1961 until 2008 with different variations in shield. Victorinox Pioneer is the civilian version of the Soldier model, which could be bought from the stores and was intended for everyone who's not in the military. You most likely saw a Pioneer in some odd color, but actual Soldiers only came in silver (for the most part) and they came in red from 1961 to 1965, and these are some of the rarest and collectible SAKs out there, if you find one in the right condition. Check out sloth's link above for more info.
Also, what about a red cadet with black badge? Is that a thing?
There are various model in the 84mm size in red, but all of them come with a red shield. You could be thinking about the opposite - a black Cadet with a red shield:
These are exclusive to a Danish store called TheGoodStuffShop:
Once you convert to dollars, add shipping and subtract taxes, it comes out to about 50-60$. It's a good buy in my opinion, but I would say that for any Cadet
That's really a Pioneer. I think he threw in the "soldier" bit just to be there as a keyword for searches. If you like that one, he has a ton more for sale at www.swissbianco.com