A few weeks ago, I cut a bunch of popping bug heads out of foam. Most of the foam I used was the soles of flip-flops and packaging foam sheet.
I made cutters out of .357 Mag and .44 Mag cases. Pop out the primer with a nail or punch then drill the primer pocket to accept a 1/8" machine screw to chuck into your electric drill or drill press.(preferred) I wish I had a 20MM and maybe a 30MM case for larger bodies. I have one cutter I made out of 5/8" tubing but it is sooo much easier to use a cartridge case.CAUTION! Use fired ammo only. (The primer should be dented)
I made a punch type cutter for foam spiders using a .44Mag case that I had squeezed into sort of a tear drop shape. I cut the bodies out of packaging foam and color them with a Sharpie or just leave them white. Just lay the foam on a cutting board and use the home made cutter like a bisquit cutter.
To shape the heads, you'll need to make another tool. I make a turning post out of a 1" long dry wall screw with the head removed. I use this in my Moto-Tool. Insert it into the middle of the foam blank cut with the cartridge case cutters described above. I use an emery nail file to cut the body shapes. CAUTION: Wear a dusk mask and eye protection while turning these bodies.Your wife will definitely appreciate it if you do the turning outdoors.