Kahn explained his reasoning to both Hector and Venessa in their respective meetings on why his plan was detrimental to their end goal.
That no matter what happened… nobody in this empire would stand up for humans even if they were brutally slaughtered since they didn't make up even 5% of the empire's population.
But if they started off with Oakenshield's route, they would be able to thoroughly smear the name of the second prince first and everyone will be against him.
And after this cruel act of his was revealed… they would make the biggest impact as the one to voice for the helpless would appear as a savior of the weak and the public opinion as well as the support from other clans who wanted to look good and righteous on the surface would obviously take their side.
Eventually, it would end up helping the said party to solidify their claim to the throne.