Polyester sleeved Kevlar makes a good shoelace.

A diameter of 1.65 mm puts it in the same neighborhood as Type I Paracord, but with a little over twice the tensile strength. It fits through more eyelets than the typical Type III Paracord, making it appropriate for a wider range of footwear. It holds knots well, will pop through zip-ties in a jiffy, and the inner Kevlar can be broken down into three strands. I buy it from TwinLine.