Using the safety deposit box in the Milford Plaza is, imho, a total non-runner as there are ridiculous queues at most times of the day at their reception desks - so much so that they don't require guests to check out. The queues are unsurprising given that they have 3 or 4 desks for a total of 1300 rooms.
For what its worth, I think you would be crazy to bring a large sum of cash to NY (or any other large city), particularly as you say that you're paranoid about being robbed on holidays . Much easier and safer to preload a credit card and use ATM's even if exchange rates might fluctuate marginally in the meantime.