A slightly oblique response: I too ended up with a number of scions in the fridge, (actually belonging to somebody else, whom I thought was going to come and "park" them on my trees). By the time I determined that they weren't coming, and did it myself, it was mid-June. I grafted them largely with simple whip and tongue grafts, and a few bark flap grafts. They have budded out within the past week, and almost all of them (roughly 30 cultivars), are growing.
Somewhat related: I had also asked a friend for scion wood of a particular cultivar. He didn't get around to cutting it until it had broken dormancy, and delivered it to me, as i recall, around June 10. At the time I got it, it had large green buds, almost leaves. I had a similar situation a number of years ago after a bun fight with Agriculture Canada, who blocked my order for scion wood on the principle that I was not "a bona fide researcher". By the time we worked this through, and got the material released, these sticks had actual small leaves. In both instances, I wrapped the entire stick of scion wood with Parafilm, covering over the growing buds, and including the tip, to seal the scion, and stop it drying out before it could heal in. And I can report that in both instances the grafts took and grew vigorously.
Broomholm OrchardZone 5b in Nova Scotia