Yes it will be a catenary but it is not a problem if the purpose is to mark the ground.

If the purpose is also to measure the distance between the 'pegs' and one uses the length of the cable in between, then it can be a problem. That's why survey chains are expensive.

If we get real picky, no physical method will really be accurate because straight line is a mathematical abstraction. It can only be approximated in the physical world, much like a circle.

Light paths come closest, although they 'bend', they bend in a way that is 'straight' with respect to space-time.