What a great family trip that must've been with kayaks on 1000 Island, Steve. Someday the kids will fully appreciate the uniqueness of that.
Based on the following trip summary, I think you'll be fine taking the PCT high trail or the Shadow Lake Trail early this year. I would stay out of the River trail due to water and bugs. This would be much better as an ultralight backpack trip. It will be a very long day hike returning in the dark most likely.
Last Memorial Weekend I caught the 7am first bus of the season down to Agnew Meadows to fill in a short section of JMT from Shadow Lake to Red's Meadow. The north slopes around Shadow Lake and Rosalie Lake had snow. Traversing switchbacks on steep snow was dicey in a few spots, but I was able to kick-step straight up safer and quicker. The rest of the trail was patchy snow in shady areas and dry anywhere the sun hit. I had a closed campground all to myself for the night at Red's Meadow, but I digress, you're not headed that way.
If you have time, do a day hike to Rainbow Falls and Devil's Postpile. Best rainbows are in the afternoon.
This is best shot of snow conditions I have from that trip, taken at Rosalie Lake. North slopes had complete snow cover, but not very deep.