Bear in mind that the AE incurred will only be high local to where you annexed. To your neighbours it will be small, maybe only 1 or 2.
You then lose 2 AE per province released as a vassal. But that is not localised, it applies regardless of distance to all Europe and Asia.
You can even end up with an overall reduction in AE, at least to the nations you care about back home.
Also, you can soak up a lot of that local AE by allying with nearby nations that you'd rather not get AE with. You can cancel the alliance after the war. Your relations will be lower than now as a result of cancelling a alliance, but very likely higher than if yyou'd not allied and they'd received full AE.
Of course if the war is already started you may not now be able to get those allies. We least you can boost relations and gift etc