Lake McConauay? We have been there many time.
Try 65 psi. If that doesn't work then you can go down to about 40 psi. You should be okay. Just DON'T spin the tires, manage speed, sometimes slow some times a little quicker. Use low range always. And, carry a chain, someone will give you a tow if necessary, I think you will be just fine. Shovel, well, I don't believe in getting stuck.
I have been to the east coast beaches and lets say its different, the rules, well...
BTW, there is not much beach, we were there a couple of weeks ago and it was near max pool. On the east end there was some beach, not much, but the crowds should be gone for the most part. West, at Sand Point there was some beach, very limited.
Have a good trip.
Rick