[Garen LiLorian]

This seems like a strange discussion to me. If the question is who would take over the forces of Mordor if Sauron should fall, I'd say Saruman. I'll justify that in a minute.

However, if the question is who did Sauron designate his second-in-command, I think the question has no answer. Sauron is a heavenly entity, unlike everyone under his command. He didn't allow his servants free will to carry out their own initiative, they did exactly what they were told at all times. Sauron was in command, and all others are tools that he used. There was no "executive officer." The closest there is to a chain of command is in the military, where Gothmog took control when the witch king died. But certainly the witch king couldn't have existed without the will of Sauron to back him, (if the works of the Elven rings, which weren't bound to the One, faded when it was destroyed, certainly the power of the Nine were broken as well) and the Mouth was a messenger, not a power. It's right there in his title.

I personally think that, had Sauron won, the Mouth would not have been given Isengard, because when all's said and done, he's got wraiths who are entirely subservient to his will to carry out his whims. No need to rely on a mere human.

However, if, hypothetically, Sauron simply vanished (and his forces didn't scatter when his will broke) I think Saruman would have taken control of the forces of Mordor minus the Ringwraiths, who simply cannot exist without Sauron. That's kind of what Saruman is going for all along. He wants the Ring, of course, but he wants it so that he can take the power of Mordor and enforce his "new world order" on the West. If you're looking to fill a power vaccuum, Saruman's your man.