No need to do anything, actually.
Players can belong to any number of leagues. So you could create a separate league and add the players playing in your "pick up" game.
But easier than that is to simply not select a league for the "pick up" game (on the Game tab - leave League set to <None>).
So long as your actual league tournaments have a league set (again, on the Game tab), you can use a filter on the Stats page to total up only those tournaments that are part of the league.