I used this technique, learned long ago, when threading 3/8" bungee through a 5/16" hole on my Hobie TI this afternoon.
When you cut the bungee, you're left with a bunch of loose outer wrapping.
Fold the outer wrapping back on itself revealing a length of the rubber core. Cut off at least an inch.
Now bring the outer wrapping back forward and twist so you can get it through the hole in the fitting. If you're going to thread the bungee through multiple fittings, super glue can be used to harden the twisted end into a threading needle.
Once threaded, you can cut off the end and heat melt the frayed ends.
