I think I would still go with "die". In spoken, everyday language, you're right, most people say "dice" whether it's one or two, but my vague memory of board game instructions is that they always spoke of the "die" when there was only one.

In BE it is now normal to use "dice" as the singular, although you always get people who would disagree!

dice /das/ noun, verb
noun (pl. dice)
1 (also die especially in NAmE) [C] a small cube of wood, plastic, etc., with a different number of spots on each of its sides, used in games of chance: a pair of dice to roll / throw / shake the dice (figurative) It was a last desperate throw of the dice to save his marriage.
2 [U] a game played with dice: We played dice all night.
(OALD)

Fowler's 3rd ed.
The small cubes with faces bearing 1-6 spots ... are the dice (pl.) and one of them is also called a [i)dice.

Ambrose Bierce:
Die, n. The singular of "dice." We seldom hear the word, because there is a prohibitory proverb, "Never say die."

Despite CM2DD's sources, I'd still go with "die". Memebers of my family are among those "people who would disagree". Quite frankly, I'd rather get on with the game than listen to them fulminating;-).

Note that it says "die" is more common in the USA, too.

Looking at our board games, the only one which has one die/dice is Pictionary (UK), and it says: "The Picturists roll the die". I guess it's also simply to avoid being hassled by purists.

Alright then, die it is. Since the game is designed to help children learn their letters, a purist approach is probably best.