On a similar note to my earlier idea about designations, here is a follow up idea I had in mind.
(This would also increase the usefulness of soap!)
First, it would be an actively learnable skill, like most others, IE, the poor sod of a dwarf that gets stuck on latrine duty may not like it, but after 2 years he or she is a pro with a scrubbing brush! Same as most other skills, effectwise, the higher the skill, the faster and more efficiently they clean. The basic brushing process would require a bucket of water, a lump or bar of soap, and a brush (craftable by crafters of either the wood, bone, stone, or perhaps even metal variaties, and a piece of hair off any animal/sentient being (yes, if all else fails, they can cut their own hair to make brushes with, if the butcher shop is coming up empty on hair drops)
Also, for any dabbling or perhaps a higher ranking might be needed (9 or 10 and up, maybe?) a new device would be enabled. The dwarven portable power pump would require either carpentry or metalsmithing to make the housing and the nozzle/pump pieces, and one set of mechanisms of stone or metal nature, and it would require it to be filled with water, and a liquid variant of soap available in the soapmakers workshop.
This would be the only one available for cleaning outside areas (water spray to soak stuff into the ground) and for a wider range of cleaning radius when used indoors(At a potentially much faster speed, however, the supply of water in the pump would wear out very quickly and require a refill, and the soap when used indoors would go quickly as well. So per-area, it would take more soap or water, but the speed it would give could definately make it worthwhile.
And if cornered while carrying one of these around, the dwarf could attempt to temporarrily blind or slow his attacker, muddying the ground or making the stone floors quite slick, or attempting to spray them in the eyes.