From my experience braided cords (with or without a core) are stretchier than twisted cord or twisted rope. The exception is whipping twine, which can be quite expensive. It's usually waxed and out of polyester
In general, look for a dense twist and a dense, non-fluffy texture. However, you will not get around sampling.
I've made good experiences with standard twisted polyester (recycling or fresh) packing cord or packing twine. In my country they sell these in the household department of most general stores right beside the paper, pens, glue and scotch tape. Buy once the whole sortiment and you should have at least one with low stretch
And they also come in different colors!
A dense braid made with high tension will also reduce the stretch of the final piece but will require some training and usually creates blisters on your fingers.