-
Isn’t there a risk something as hard as that will damage the inside of the frame?
No, none at all - it's tiny. The diameter of the centre section is less than the diameter of the hoses attached to each end, and only a few mm long, so there's no realistic way it's going to hit any part of the inside of the frame. Due to its diminutive size it's a right PITA to install and remove, and annoyingly easy to misplace, but it works really rather well.
Or chop the ends off the old hose, join the new hose to the old hose with one of these:
and use the old hose to pull the new hose through.