If I remember for my H356 the specs for running rigging were mostly Yacht Braid or some other double braided cordage. For many of the lines that was too stretchy. Specifically I'm talking about the furling line for in mast furling, or the outhaul for conventional sails, and halyards (Which need to be Ultra Low Stretch).
So, my point is that running rigging specs are skewed more towards economics than towards ideal. So if you are going to replace running rigging do the research and pick the best balance between performance and price for you.
Don't underestimate the positive effect good cordage can make in the fun of sailing. With stretchy mainsail control lines when a gust hits the sail will balloon a bit, and the boat will heel over while the sail creates drag and the rudder drags acting as a brake. The helms person would feel the boat is a slug. With less stretch, when the gust hits, the sails stay trimmed, the boat heels, and then accelerates and comes back up with more speed. The helms person smiles. Hugh difference.
And then there's the handling aspect. Sheets are nice if they don't knuckle as easily, especially if they are on and off winches. Spinnaker sheets should float. Some low stretch lines are too stiff to go around blocks without undue friction.
Don't just