I haven't used it, but for this project I would try out Terial Magic. You would cut the shirts first, then dip the flat fabric in Terial and allow to dry before ironing (I think). It is supposed to stiffen fabric to a cardboard feel but washes out completely later. I think it is used for fashioning fabric flowers (not washed, of course!) and other types of projects. I'm thinking it would work better for nylon shirts than an iron-on interfacing, simply because nylon often cannot take enough heat for a fusible to work. Anyway, I'd get a bottle and try it out. Here's a link to it on Amazon:
https://www.amazon.com/Terial-Arts-M...dp/B00KIFBMKO/