Stress the problems with faux leather, such as unknown durability,
your lack of control or guarantee for it, what it will do when
soaked with perspiration, etc.
Why not use a good old 'leather shoe lace'. They are available in
long lengths & last a looong time even when used in boots that are
used on a daily basis. I'd imagine a suitable dye could be found if
the natural color of the lace isn't acceptable.