Well that's certainly an option. And there is alot to be said for Duke Abraham. He's catholic, like you and the majority of the citizenry now *wink,* he's absoulely loyal to you as he's your cousin, so no marrying your sister for him. In fact he agrees with your governmental course completely, so much so that he can almost be considered an extension of your own will.
He's great, but not exactly perfect. He lacks any sort of legitimacy with his new nations existing aristocracy. In fact, they see right through him immediately and treat him as if he were nothing more than a puppet lord, and that living under his rule is treated exactly the same as living under yours. Even the Catholic lords are resentful of this impetuous outsider or upjumped quisling being put in charge of their great nation, a mockery of their generations of history and tradition. Sure they give him lip service because they fear reprisal from your army, except when they don't and then seperatists rise up in rebellion. Taxes are collected inefficiently, and while he has access to the manpower pool represented by the willing and able peasantry, he has to depend on your government to train them and outfit them with gear and an officer core. What's worse, since he lacks the wide spread support of the government he pretends to represent, he is unable to make any headway in swaying the minds of his people towards the ultimate goal of accepting assimilation into your empire. If you want this nation to assimilate, any progress will have be done on your end.
It's a shame, had you appointed the Shah in Exile your history of conflict and his refusal to bend the knee to your catholic god would have worked for you, it would have reassured the people you had no immediate intentions to rob them of their independence. And with that reassurance they would have opened their minds to what your diplomats had to say. It may have taken 10 years, but in that time you could have kindled a great deal of love between your people and his, you may even have convinced them to do the majority of the administrative work necessary to finally bring your people together permanently. I'm not saying that wouldn't have taken a great deal of convincing, your diplomatic core would have been working day and night guiding the process. But your precious administrators would have been free for other tasks.
In short, there is already a way to represent an illegitimate pretender placed on the throne of a nation by a foreign power. It's done by simply owning the provinces without coring them and having a feudal monarchy.
There's also already a way to represent intelligently constructing the government of a subject nation to your own specifications, but it requires a great deal of diplomatic acumen. You'll probably learn the ins and outs about the same time you figure out how to use limes to combat scurvy.