Nice idea, but chutes tend to be quite large to carry.
My parachute with an 8m diameter weighs on my not-very-accurate bathroom scales about 3kg. I can just get it into a gymn bag - so that's about 35x30x20cm. Better off carrying a tarp or tent.
However what about creating a 4m canopy with fewer bits of paracord running through it and less material. Make it like a four sided teepee was what I started to think about, then I started to think about how many panels it would take to make such a beast, hence the statement about "widths". I was talking about parasilk on the roll, what is the maximum width you can buy it in?
Genuine parachute nylon as required from one U.S. Federal procurement agency has to be 58 and 1/2 inch wide.
Someone on e-bay is offering "parachute nylon" at 38 inches wide.
Just for interest, here is a pdf documents with the specs for official parachute nylon - or at least one type of it.