A few problems with the idea of a UN fleet to deter aggression:I think it's a great idea but generally unrealistic.
Agree with Feanor's comment regarding the UN spearheading this. UN could simply ask/assess larger membership fees to nations starting with the members of the UN Security Council.
If they become UN ships they I'd ask a further UN question, why limit them to disaster relief?
Why not set them up as a UN unit to deter potential aggression with an international force?
Float them toward the coastline as conflict arises and provide international deterrence as a negotiation tool?
1. The UN is not currently tasked nor organized to "deter aggression".
1a. Nor are they probably competent enough to pull it off (IMHO).
1b. There is a huge amount of leeriness and fear in certain parts of the world about the loss of sovereignty of the UN doing exactly whast you propose.
1c. Good luck getting the UNSC to agree to fund it. Especially in the assessing larger fees section.
As far as the UN setting up something
Now, as Feanor mentioned, the Russians could do it-it would make some sense to have something like these assigned to MChS (although no one would believe that they would just stay MChS for long), but Russia's unique in that they have a national organization for this. Most people don't. The equivalent UN office, OCHA, is neither manned nor equipped to drive ships. Nor do they want to be-their goal is to be a facilitator for national-level agencies to provide expertise and equipment and to be able to respond quickly as needed. And they're pretty good at that; if pressed into the role of being a resource provider, I can't imagine they'd do well at it.