Keep the scionwood dormant in a fridge until you have a stretch of warm days coming up. I’ve only grafted peach one year now and I used advice from this thread: Optimal field grafting times in spring and it went well. The rootstock trees had (small) leaves and about 5 days of highs in the 75ish range and no freezing nights. Around petal fall is recommended for stone fruit, but my weather did not cooperate with that.
I can’t remember exactly, but I think I’ve had freezing temps every year I’ve grafted, after grafting - not long hard freezes but temps that dip to the high 20s overnight. I never even considered it might be a problem but I imagine it could be if it was a hard frost.
This might also be a helpful resource for grafting stone fruit: https://purvisnurseryandorchard.weebly.com/uploads/4/6/2/3/46237531/sidegraftforstonefruit_purvis_nafex.pdf