I don't see Water/Steel as viable: Arghonaut has more metal appendages than Privatyke, and is not a Steel-type. I know Scratchet and Voodoll are part Normal, but a Normal type changing to something else is not common among official Pokémon, and Privatyke does not look especially "Normal". Water/Dark is somewhat interesting, but again, Arghonaut feels even more Dark than Privatyke.
I guess another potential option would be pure Fighting; that is, interpreting Privatyke's immature octopus look as it not being used to the sea yet. Both Water and Water/Fighting feel more sensible, though.