Strictly depends on your experience in big, fast water w/real consequences. 37k is "safe" but real pushy, you will have no time to make decisions and better hit the scouts for BD2 and BD3 - or know where you're going. "The Claw" - aka Big Drop 2 1/2 - will complicate matters... significantly! Right run in BD3 will be there but the laterals off the right side will scare you.
The North Sea (from Rapid 2 to 5) will be out, not as huge as it gets over 60k but starting to get rambunctious. I've seen eddy fences in there so high you cannot break through them with a raft - any raft. (I had a hard time in a kayak many years ago at 70k+, couldn't hit an eddy until below #5).
If it wasn't for houseguests I'd love to be there. 37k is serious, make no mistake. You will not want a swimmer and if you flip anywhere it will be a LONG time before you can get to shore. I've boated around the world for 40+ years - Cat above 30k or so is genuine Class IV, not only for the water/rapids but because if someone is hurt it's a long way/long time for evac. NPS will almost certainly be there, they like to hang out on right side below BD3 - but hope you don't need their tender ministrations, and you can't count on 'em in any event.
But "safe" - depends on your experience. With zero in Cat, bet you won't need to bring a groover...