Problem with shroud attachment

[Brion Toss]

Hello,
The stainless rivet will work, and will be fairly strong in shear, as well as secure laterally. Hard to remove, though, and not as strong as a screw. A stainless helicoil installation might be preferable. Easy to install, and quite strong. Or a Riv-Nut could work: a blind rivet with a threaded interior. You set it in the mast with a specialized tool, then install an ordinary machine screw. Nifty.
Any of the above will work, and in deciding, it might be good to begin by analyzing what the screw is supposed to do. In this case, it and its fellows distribute the shroud load to more mast molecules, taking some of the load off that bolt. For this reason, doing nothing, and just letting the current screw float in its corroded hole might not be the best course, as it won't -- quite -- bear a full share of the load. Plus, as you mention, there's always the possibility that it will fall out someday.
Fair leads,
Brion Toss