Sure that is fine to do. I don't do it but it sounds convenient to me too. When not in a hurry I often shave in the bathtub using a hand mirror yet get up to rinse the blade in the sink.
i always do that.i put shampoo in my hair then i rinse it out then i put my conditioner in and keep it in then i brush my theeth then i shave my legs then my arms then my arm pits then my pussy then i wash my body and my pussy then i rinse everything out.