Only the very first Tiger I's deployed to Lennigrad were painted in Pz Grey. Tanks were painted at the factory, and there would be no reason for a unit to paint its tanks grey in the field. In addition, seeing as you want to be accurate, that Tiger you have alos needs Zimmerite, which i am guessing the kit does not include.
If you want to stick with this scale, Tamiya did an early production Tiger I, that can be done in grey and no zimm needed.