Can I activate and resolve Hand Destruction with less than 2 cards in one's hand?
No. You cannot as it states specifically:


  Each player sends 2 


This means the number of cards is mandatory if any player has any less then the card cannot be activated.

On the other side, if a chained effect dropped you or an opponent to less than 2 cards in hand, then Hand Destruction would resolve without effect as the initial requirement is that you send 2 cards to the graveyard.

If it said up to 2 cards, then you would be able to use it.