Mrs. J: FloorDry from autozone is 100% natural DE. You are welcome to read the whole thread if you are interested in using DE as a seed starting medium and learning about its benefits and drawbacks. There are nearly 900 posts in this thread
Ray: your answer to my question is helpful in teaching those who are thinking about this process with root-sensitive seeds, and why they should try other methods, so they can avoid the mistake I made. When I posted my question, I had already sowed the seeds in DE. As such, I was looking for ideas on how to safely transplant them into either their final destination or an intermediary pot with regular potting mix, now that they've germinated since I realized the mistake. I was probably not clear about that. Would be easy to resow properly if I had more of the seeds, but I do not.
The trays have a hole in the bottom, I'll just try sticking something from below and maybe they'll pop out in one go once they are ready, and hope for the best.
EDIT: to clarify, I'm trying to figure out how to get the cucumber and squash seedlings out of the seed starting tray filled with DE, with minimal disruption to the roots.