I was thinking of some 3 strand Marlow line or some 3 strand polyester rope. It often comes as small as 4mm. Any 3 strand line actually. You could even just go get some at a hardware store. Although, I might avoid nylon unless you like splinters. Color might be the only issue at a hardware store.
I say three strand because then you can do a 3 strand eye splice so you don't have a big knot running through the pulleys all the time.
I had a second thought about the marine supply stores though. They tend to sell in bulk by the reel so it would be costly and you would end up with 300' plus. Maybe you could go into the screen retractor business???
I'll fire my buddy off an email to see if he has 20' scraps of 4 to 6 mm black line laying around, just in case.
