I slept on it and realized I was thinking of a dwarven washing device more than a simple toilet. Too complicated, I agree. However, a 1x2 workshop with the requirement that it be built over an empty space (like a well), that's much more possible. Have the dwarf sit on a "throne" positioned above the empty space for a moment or two to produce a happy thought (some thing like "Urist McDonepooping had a good bowel movement lately"), then pull the lever to complete the process. What is produced is one of two new materials, 50% chance of either: Either a new liquid called "urine" or a new slime called "dwarf pellets" or just "feces". These are produced by the "throne" every time the lever is pulled, dropping through the hole below it to wherever. I'd suggest the material have the same qualities as potash, except being liquid, so that any farmers wishing to use it for fertilizer has to gather it in a bucket, like lye or milk. I'd also add the "can rot" quality to it. Since the loo will always be above this substance, even loos that drop outside the fortifications will leave a heap of miasma generating material below. Bat guano creates crystals of saltpeter when it rots, perhaps the end reaction of the dwarf pellets rotting is that it becomes a crystal of saltpeter as well, to be collected for your gunpowder mill? Either that, or the pellets become a consumed reagent in the ashery (to make potash/pearlash) and the powder mill (in place of potassium nitrate). Also, it would make more sense if the dwarves got an unhappy thought from the lack of toilets rather than the lack of chairs, wouldn't it?
(Perhaps toilets are a class of chair that must be designed by an architect over a hole, and that produces two happy thoughts ("admires a fine toilet" and "had a good bowel movement") and a dwarf pellet when used?) Required materials: 1 "throne", 1 "mechanisms", 1 "empty tile".
I can imagine a "holding pit" where trapped elves scream with fury at being rained with dwarf pellets from the holes above them.