The Cameo Silhouette will cut metal foil, and I suspect the Cricut will perform in a similar manner. Metal foil will certainly be heat resistant and also quite opaque where needed. It's likely you'll have to paint the foil black before cutting.
Amazon has a wide selection of foils that I'll use as examples. The first one of note on the list is 12" wide, 30" long and 0.005" thick (0.127 mm) and may be the top choice for your project. There are 38 gauge sheet offerings, but that's 0.006"/0.152mm, slightly thicker. Another entry is a meter long, 100 mm wide and 0.03 mm thick, which may be easier to cut.
Cutting metal foil/sheet is going to create a dull blade, but the brass and aluminum offerings are going to be softer than the steel of the blade and may last a sufficient time for your purposes. You'll know when it's time to replace the blade when it tears instead of cutting.
If you aren't wedded to the idea of using the craft cutter, consider that one could hammer a series of nails into a suitable plank. Selecting various diameter nails would provide the variation of hole sizes required, and it would be important to drive them into the plank in such a manner that the protrusions are of uniform length. The support surface for the foil could be a softwood or a fairly hard foam, with the plank being shifted between foils to prevent the hole depth from becoming excessive.
Laser cutting metal = expensive to purchase, not all that cheap to farm out. My CO2 laser will not cut metal of any "thin-ness" and a fiber laser runs into the mid-to-high four digits.
My travels for more information leads me to leather punch sets with hole sizes from 1/8" to 1" depending on the set selected. Image from link:

If you're going to turn it into a mass production sort of build, more than one punch set installed in the plank would provide for some variation. I'd suggest a lever-type press rather than a hammer to apply the necessary cutting force. I can envision placing the plank, dropping the press, lifting the press, rotating the work piece to a different orientation and performing the sequence again.
I've worked in a print shop environment where the huge paper cutting blade performed its task with a piece of HDPE under the entire length. It provides for a solid cut and can take repeated cuts without replacement needed. End grain hard wood cutting boards may serve as well.