I’d imagine that some portion of the world’s navies would still be required for stuff like piracy suppression (historically always a major mission for navies, FWIW), but that might be a handful of destroyers or frigates from each nation at most.
A few other assets like aircraft carriers, amphibious assault ships, etc… might be repurposed as disaster assistance ships- something like an amphibious transport dock (LPD - San Antonio class) might be a fantastic option- it’s got space for helicopters AND hovercraft, as well as a lot of hold space for heavy equipment and/or supplies. Keeping 3-4 of those around and stationed around the world might go a long way toward mitigating a lot of disasters.
In addition, militaries, especially the US military, have a LOT of field logistical capability that would be folly to just draw down. It’s the rare organization that has the ability to supply a force of tens, if not thousands of people thousands of miles away to fight a war for an unspecified period. Again, that could be a real asset for humanitarian purposes.
I would think that we could use the US national guard internal deployments as a guide as to what’s actually useful and effective as far as types of troops and what they’d need to do. In fact, maybe keep the national guard around for that purpose, and get rid of most of the active-duty component, except the naval ones.