This is a great discussion. One point I'm not convinced on, though, is that a sica was a strongly defined type of blade. We could be dealing something similar to the English "knife" or the Chinese/Burmese/etc. "dao," where the term is loosely defined, but (as always) everyone in the culture knows what one looks like.
I'm guessing that we can add "sica" to this group of general blade terms. This contrasts with terms like "gladius," which seems to be a strongly defined, two-edged military short sword used by the infantry.
"Sicarius" makes sense as a category, too. After all, in English we have gunmen, hatchetmen, hired knives, etc. The term "Sicarius" seems to belong to the same category. Terms like hatchetman are a bit different from, say, swordsman or gladiator, after all.
My 0.02 denarii,
Fearn