Before vowing to carry a large, sharp knife on your person:
try to cut a piece of mainsheet, jibsheet, spinsheet or bungee with it. Then try it under duress, being dragged, or hanging upside down. It ain't so easy. Some of these modern (Kevlar-containing?) lines are very difficult to cut.

Check it out, even nipping off a bit of your new line- to have a fair idea what, and how fast, and even IF it can be done! The life you save could be your own-or your kid's.