I don't know what program you're using for to make the skins, but you might want to run a noise filter on the main white areas then a slight blur. This will help break up the look of the plane so it doesn't look solid (gives it more of a speckled, fabric look).
What I do in Gimp for fabric is:
1. Create a new layer and fill this with a fairly neutral gray.
2. Create a layer and apply Noise -> Hurl (increase the density)
3. Desaturate this layer and Duplicate it
4. On one layer, apply a Motion Blur at 90 degrees. Play with your length until you get it where you want it.
5. On the second layer, apply a Motion Blur at 0 degrees at the same length.
6. Adjust the transparency of your two blurred layers until they're about where you want them.
7. Once you have they where you want them, merge them with your neutral layer.
8. Select the layer with those elements on which you want the fabric texture to appear.
9. Go to Filter -> Map -> Bump Map
10. Use your merged "fabric" as the Bump Map, play around with the other settings as desired (I prefer Spherical or Sinusoidal for the map type.
11. Apply this, and you'll have a fairly nice "woven" texture to the surface.
12. Make sure to use your "fabric" texture on your actual bump map, as well.
In order to make sure you don't lose any of the texture along the edges, I would make your fabric texture fill the entire image, and then selectively apply it the the layers you want textured