You cannot have it both ways...
You cannot pull out your corporate account if the age issue comes up on an Expedia reservation.
Corporate rates are usually higher than what you can get outside as they are negotiated upfront and dont fluctuate with season and/or availability. Also, when you book at a corporate rate and are travelling on business, insurance is part of the rate - which is not the case when you book a car/van on Expedia or elsewhere. If you add insurance + rental booking on expedia, is it still cheaper than the corporate rate?
A word of caution: if this is for business travel, your company folks may frown upon you if you dont book on corporate rate and get into an accident. You may be stuck with the bill as they are not obligated to cover you as per policy.