Dice with same letter on each side
What ended up happening was as follows. I first pre-arranged the letters well ahead of time by myself. Luckily, the other person needed to go into another room for some reason. I used this opportunity to suggest that we play Boggle, which was agreed to. I then quickly got the game ready. When the other person returned, I claimed that I had already shaken it up. It worked out nicely.

Because they left the room, I didn't have to deal with the problems I mentioned, such as suggesting that I be the one to shake the letters up and then trying to fake doing so, but in a convincing manner.