I don't really think Tsüor has a soul (he can't seem to grasp paradoxes, as we have seen -- the paradoxical joking of the Skin-Eaters in TJE being one example...although that could just be a purposeful charade, but I doubt it). I do, however, definitely believe that the whole "skin-spy with a soul" concept will be important later on, and that it's actually not an "anomaly", but an intentional creation by the Consult that is perhaps extremely difficult to produce, or is for some reason a limited resource. I feel the situation with the original Mandate Grandmaster (can't remember his name, the one Maithanet reveals and kills) being an ensouled skin-spy was more of an early indicator that such creatures are actually possible, since in the grand scheme of things it really didn't seem have much significance plotwise...aside from showing off some early Maithanet-badassery (and who doesn't want as much of that as possible?).
I also think there's the possibility of an ensouled sranc, or perhaps more likely, an Ursranc. Given the brief sranc-chieftain's POV from the WLW (which came off as a barely cognizant, idiotic beast whose internal thoughts consisted primarily of KILL-MURDER-FUCK"), it seems really, really weird to me that a being of such power as Mekeritrig would use one a regular old sranc as his freaking elju, a responsibility (a privilege even, to some) of enormous importance the Erratic in question. I mean this guy is the main Nonman representative of the Consult, and one of the four agencies that forms its entire leadership (along with Shauriatas, Aurax, and Aurang).
This could just be chalked up to conditioning/training of the sranc-elju, or perhaps even a bit of early world-building inconsistency, which we already have at least one example of in that prologue section.