The hot part of a Vapcap is the cap. The cap cools down very quickly, within just a few seconds after the cooling click I can remove the cap with my fingers, so they can be concealed quickly if needed. There are several Vapcap storage devices besides the Dynastash that are small and can fit in a pocket.
One is the Silo by Interplanetary Development.
https://www.interplanetarydevelopment.com/collections/accessories/products/silo-xl
They can accommodate a regular Vapvap or the XL, plus a small herb stash.
@Ratchett makes a very nice soft leather Vapcap pouch. It will hold three things; two Vapcaps and a lighter or one Vapcapcap, one stash doob tube and a lighter.
Here's mine with a Copper Stoned Vapcap XLS, a doob tube for flower and my Aomai flint jet lighter.
Sure you can, but I'd rather use an organic material if at all possible. Hopefully your Japanese cotton is organic.