Applying " both players discard 2 cards" and "then draw 2 cards" are not treated as being done at the same time.
Your opponent chooses whether or not to apply "Your opponent can discard 1 card to negate this card's effect" when resolving "Dark Scheme". (If your opponent discards, that card is treated as being discarded by the effect of the player who activated "Dark Scheme".)
If either player doesn't have 2 or more cards in their hand, "Dark Scheme" cannot be activated. Also, if either player has 1 or fewer cards in their hand due to an effect activated in Chain to "Dark Scheme", the effect of "Dark Scheme" is not applied.