The two goals are not mutually exclusive, and they are quite narrow in scope. For all we know, the Inquisition needs to flex its political power instead of just its military might, and WEWH is a natural followup to the small-scale political maneuvering the Inquisition has already been doing. In addition, the Inquisitor and their advisors understand the nature of political alliances, and can't afford not to make any in Orlais, so it's a double-bind of sorts. Corypheus, on the other hand, basically wants a puppet, weak leader, no leader, or a divided leadership causing (more or less) a resurgence of the civil war in Orlais in order to seize control or just keep Orlais out of the conflict long enough to maximize the impact of his Warden+demon+Fade army, and any combination of leaders that you can support could theoretically fall to those circumstances without Inquisition support. TLDR: There's much more going on than meets the eye, and all parties know this.