What's this for? A better doubled over condom, for drug mules?
I would not go with button cells as such, but something like 1/3AAA cell.
Yes.
Why do you have to use nylon, and not (for example) hot-melt-glue?
Useless. Caps of a worthwhile size are HUGE, compared to what you are aiming at.
And this is where you find another client, if this one won't negotiate. Small button cells are low current. (generally)
Have you ruled out pyro devices? There exist several mixtures that will on being heated to 100C or so, heat themselves to 300C quite easily. This could dramatically cut your power needs. Ask over on sci.chem
Your first step is the batterys. What is the maximum size (button cells go all the way from about 5*1mm to
30*4mm). Now, go away and find the impedance of those cells. I'd be really surprised if you could get 7W out of anything smaller than 1/2AAA.And sound triggering may be fairly simple - can you use an ultrasound machine to trigger them? Hmm. Images of glass toroids, with the string tied to them shattering when hit by ultrasound emerge.