Maybe perhaps... the spray could add cross-links to a streched polymer film.
So you would produce a polymer that still contains available functions, make a film of it - better streched in both directions like Mylar is - then spray on it a chemical that brings shorter cross-links between the film's naked functions, and the cross-links would shrink the film.
Ahum...(1) I'm not a chemist (2) This scenario is far fetched (3) Why would cross-linking shrink the two streched dimensions and not the thickness? (4) Etc and so on and so forth.
Maybe a fibre makes it better. It would crimp as cross-links are made among distant locations. You can make a fabric or a felt with the fibre. Some felts are waterproof, for instance wool in traditional Bavarian clothes, so a hydrophobic fibre should make a waterproof felt.
I suggest that you experiment with an existing material that is "cured" by cross-linking and add too little hardener before stretching (hammer between paper sheets with talcum?) into a film.
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A different approach would let a component evaporate to shrink the polymer. Typically water from vegetable compounds or from polyamide. You know polyamide clothes shrink when drying. For plain material, PA6-6 shrinks by some 3% in each direction between immersed and fully dried.
Fibres seem to react more strongly in clothes. Maybe water solvates the cross-links between remote locations of the fibres, and dryness lets them bind again. This would be a source of inspiration for materials that react more strongly.
Of course, the material will soak water in bad weather, so I'd oversaturate it before, maybe with an autoclave, and keep it in water until it's used. A short polyamide like 4-6 or smaller should shrink more than a long like 12.
Or try an other liquid. Gasoline is known to swell polyolefines, so you might try a polyethylene fibre or film soaked with hexane, then look for a better pair. At least this one won't react to rain.
Marc Schaefer, aka Enthalpy