It will depend on exactly how fuzzy it is, but here's are some options:

1- If you have a propane torch with a flame spreader, you could set it for a low flame and pass it QUICKLY over the frayed area. That should knock down the worst of the fraying. You must be VERY careful to move quickly and not to allow the head of the torch to contact the skin.

2- Whether you try the above procedure or not, the next step would be to apply a coat of varnish and let it cure. There will be some fuzz poking through it, but don't worry about that. Once it has cured, take a SHARP steel or carbide scraper and carefully scrape away the protruding fibers. Varnish again and repeat as necessary until you're satisfied with the result. You'll probably want to apply a final coat to the entire boat to even out the finish.

3- After re-coating, you could try sanding lightly to remove the fuzz, rather than scraping.

If runs happen again, use a sharp scraper and SLOWLY, CAREFULLY scrape them off. There is no reason that this should damage the fabric or cause it to get fuzzy unless you rush and get too aggressive. I have done it successfully many times.