How would the combined masses of the Centaurs or the scattered disk compare to the combined mass of the asteroid belt?
According to Sheppard et al. (2000) "A Wide-Field CCD Survey for Centaurs and Kuiper Belt Objects", the total mass of the centaurs is likely around 10-4 Earth masses.

Gomes et al. (2008) "The Scattered Disk: Origins, Dynamics, and End States" estimate the mass of the scattered disc as between 0.01 and 0.1 Earth masses. (Going by the abstract, I don't have a copy of the book to check the details.)

As you noted in your question, the asteroid belt is around 4% of the mass of the Moon, or about 0.0005 Earth masses. So the centaurs have a smaller or similar mass to the asteroid belt (bearing in mind the uncertainties on the values), while the scattered disc is considerably more massive.