Guessing a 'tink' noise translates into, 'that carbon fork's a goner!'
Certainly not a good sign... although who knows? It might be fine.
If there is a crack (which I'm afraid seems likely), and you can find it, both your proposed methods of repair seem like they'd stand a pretty good chance of working, if done well.
If it turns out you have choice between adding material or removing it to fix the problem... that should be a no-brainer.