Cutting through plastic foundation wouldn't be a bad idea, I hadn't thought of it. Accomplishing that without hurting a 10-day queen cell would be a bit of a difficult trick, I'd suppose. I'll give that a try.
Sometimes removing them away from the plastic foundation does open the cell in the back, but if you are very careful with your grafting spoon, a sharpened wooden tounge depressor, or a forged flat and bent nail, or whatever scraping tool you prefer, it does not hurt them. (At $25 per queen these days, don't worry too much about damaging the comb around the QC, but DON'T DAMAGE THE QUEEN CELL). Adhere a small piece of foundation onto the opening and very carefully cover it with a "hair roller"-type queen cell protector, or your incubator queen cell hatching jar or cage.
For my queen cell hatching cages, I modify the little 50 ml bottles of hard liquor that the drunks leave along the bike path near my bee yard. I rinse them to remove the alcohol smell. An 11/16" metal tube tool burns a hole in the side for #8 hardware cloth vent, and in the bottom for a tapered cork. Into these corks, I peg a sawed-off golf tee, to which my artificial queen cell cups are attached with hot wax. I use a #59 drill through the queen cell frame bar and into the middle of the golf tee shaft for a sewing pin to hold the golf tees onto the bar. The advantage is the screw-off cap offers a beekeeper-controlled release that she can walk out of, or I can remove the cork and golf tee-mounted cell, and get her out quickly, if need be. A very small mason jar should also work, and you should add a dab of queen candy for after she hatches.
5-hole queen cages also work for hatching QC's in an incubator, and they may be easier for a wood shop skilled guy to make. Realize that I'm setting up a fairly different operation for I.I. queens, so controlled hatching is critical for me. Most queen producers don't do this...they want the queen cells in the mating nucs.
I do this cell punching on 48-hour queen cells, which are much more rugged than white-eyes pupa through purple-eyes pupa stage, for re-queening out-yards. In this case, the cells are usually made up on the queen cell frame, and the whole cell finisher colony is taken to the out-apiary for re-queening. Just remove the pin, pull out the golf tee and queen cell, and mount the 2-day cell into the middle frame of the brood nest about an inch under the top of the cluster. 48-hour-old queen cells should not be used for weak colonies.
Cell-Punch Method is usually done in fresh comb in which the queen has been isolated under an excluder partion, so that I know I have 8- to 12 hour old larvae in fresh comb. The cell containing the young grub larva is attached onto a plain QC bar with just-barely-molten wax. It is a no-graft method otherwise similar to Jay Smith/Henry Alley Cut-Cell Method. Use your search box to look up Oldtimer's 5-star thread, and also search old threads regarding Cell Punch Method.
Oh, and the metal tube was sharpened on the lathe with an O.D. grinding attachment (3 kneeling "I am not worthy" 's to my buddies who allow me G-job time in their machine shops!). A careful hand and a LIGHT TOUCH could sharpen a steel tube on a bench grinder wheel, with a file and a stone to finish, but BEEEEE CAREFUL!!! Better yet, go the the hobby shop and buy one of those super-thin-walled brass tubes, but don't bother sharpening it. It should go through new honeycomb cold as is, you could heat it to go through old, black comb.