I figured out my own method. I changed it to have two lists with 52 items, one with the cards and one that holds the corresponding "positions" of each card (1=your deck, 2=opponent's deck). At the start of each game, I need to change half of the values in the "position" list to 1 and the other half to 2. I came up with this procedure. The beginning is actually the only time you'll ever need to shuffle in War, so I can get away with assuming all the values in "position" will be 0 before the procedure is run. I tested it and it works!
The procedure puts a list of random index values into its local indexList if that idex is not already present. It then goes through every item in "position" with a matching index and sets its value to 1, then goes through "position" again and sets the rest of the values to 2.
Thanks to all that have helped me!