I've got a 10mm line, about 5m long, I think. I store it in the tramp pocket, and on the first capsize of the day tie it round the dolphin striker and then chuck it over the top hull.
I used to leave it tied round the dolphin striker, but the bowlines kept undoing themselves as they got pounded by the waves. I lost one rope this way.
I'm sure you could go thinner for weight reasons, but I'm not a big fan of putting fine lines over the hulls and then putting all my weight on them.
Paul