Unfortunately, it is not possible to remove the covering of a duck's bill. Only the tip is ceratin like the beak of most birds, but the rest is a kind of leathery skin. I prepared a few ducks and flamingos with a stuff called "L10 maceration fluid". This a chemical solution which can clean a skull of all soft tissue in about 1-2 hours, and I kept the bill above the fluid surface. Afterwards I let the bill dry and it usually stays intact (although not well protected against bugs). However, like the beaks of mounted ducks the colours will fade over time. On mounts the bills are usually painted, but in my opinion, this doesn't look very nice on skulls. In this message I'll post a few pics of such skulls. The L10 stuff can be bought at a Dutch taxidermy supplier, but unfortunately they cannot ship it to the USA.
By the way, macerating the skull with the beak above the water line won't work, the bill will rot partially and get soft and sticky, and it will keep stinking for years.