Just finished chapter 5 this morning, because I didn't have time to read over the weekend.
It would seem to me though, that at this point, Skeaös and the Emperess are not yet skin-spies. I believe that it is only after Xerius meets with Mallahet and learns of the SS's involvement, and so work against the Holy War, that the Consult moves in and starts directing things there.
Note how all of a sudden Skeaös' story changes in later chapters, where as before, here in chapter 5, he even cites the Indenture as his own idea. I would think that Emperess Istriya was replaced after Skeaös was eliminated, as well, to keep an agent in the midst of the Emperor.
The Consult wants the Holy War to succeed. Why then would the Skeaös agent not be informed of the Scarlet Spires' joining the Holy War? The Consult certainly knew by then. No, I think that it is only after Xerius learns of this in the Mallahet meeting and is actively planning to subvert the Holy War that Skeaös is replaced. I think it is just before he meets with Conphas that the substitution takes place.