35 cards are left, including 4 legs and a few of epics. All rogue epics are left which means they're either really really bad like usually they are and saved for facebook dump, slayer was like the exception that was good. Who knows, maybe they're good and add more utility to rogue hero.
They have to reveal 2 heroes and Lich King, those are likely complex cards that take more time to show and play than other cards usually take. I don't think they will be showing many cards on the stream, most of them are neutral common fillers left for facebook.
Just a reminder about the assumption that final day / facebook cards are filler, I believe these were all final day / facebook cards in Un'Goro:
Primordial Drake, Bittertide Hydra, Stubborn Gastropod, Stonehill Defender, Jeweled Macaw, Free From Amber, Radiant Elemental, Lyra the Sunshard, Earthen Scales, Primordial Glyph, Vicious Fledgling, Hallucination, Humongous Razorleaf, Biteweed, Razorpetal Lasher, Nesting Roc, Meteor, Molten Reflection, Fire Plume's Heart
how many snowflipper penguins do I need to sacrifice to not unpack any Princes
You're thinking about this the wrong way around. If you unpack a prince, that gives you exactly enough dust to craft a golden Snowflipper Penguin.