It should work, because Hand Destruction is not a cost. Hand Destruction's sent and draw happen on the same chain link, and therefor, cards like Peten, Dark World, and Jinzo Returner do not miss there timing, and will activate.
The key word in Hand Destruction's efffect is bolded: "Each player sends 2 cards from their hand to the graveyard AND draws 2 cards".
I am the master of the Yokai Deck.
Yokai V1: 25-1
Yokai V2: 13-1 (Intentional Loss to advance deck to next version)
Yokai V3: 34-1 (Intentional Loss to advance deck to next version)
Yokai V4: 6-1
Yokai V5: 18-0
UDE Player Management: Level 1
POP TO (Pokemon)
Yu-Gi-Oh Rules Comprehention Level 1
Bandai Meijin (aka Judge/TO)