DY for arguments sake assuming you are correct (as an aside gift giving on Decemebr 25th is a Western European thing, Asians exclsively give money. Though like us, in America their minhag is evolving somewhat too)
So what would be assur:
Gift giving ever?
Gift giving on Yom tov in particular?
Gift giving specificaly on chanukah: always even November/early december or only when it is near Dec 25th.