Roped In

A 1" line in 1/35 would be .028".  I would look at some braided fish line in the .030 range.  Should be supple enough to work with, and most is multi colored like climbing ropes of today.  Easy enough to color with a sharpie if needed.

I use ship rigging for rope. Not sure what size you would want. But when i needed some rope for tieing down equipment on a tank, i got a few sizes and just matched up up. From the sounds of it, you would want one of the larger sizes.