Giving Umaro's attacks to another character

Can you turn Umaro's attacks into weapons that do that desired effect?

Not without rewriting entire lines of code. The code goes a little like this, though it is drastically simplified.
1. Choose the Fight command (or have it chosen for you in Umaro's case)
2. Is the character Umaro? (this is the line that my code changes)
  a. No: Do a normal attack
  b. Yes: Continue on this list.
3. Add Attack and Charge to the list of options.
4. Check for Rage Ring in Relic Slot 1. 
5. Check for Rage Ring in Relic Slot 2.
6. If it is there, add Throw to the list of Fight options.
7. Check for Blizzard Orb in Relic Slot 1.
8. Check for Blizzard Orb in Relic Slot 2.
9. If it is there, add Storm to the list of Fight options.
10. Choose between all available options.

So, it's possible that you could have 4/5 and 7/8 look for a weapon in the R/L hand, and it might be possible to have all characters branch down this path, but it would be harder than simply changing a checkbox in FF3usME.