Will I get Articuno or Snorlax?

As long as you haven't tapped on the research breakthrough yet, it should be Snorlax if you wait until tomorrow.

BTW, waiting will render you unable to complete any more regular tasks until you've claimed the big box.

I'm not going to collect the 7th day stamp until well after 1pm on july 1st. I don't want to take any chances.