Can you discriminate a monooxygenase from other enzymatic mechanisms by the requirement of NADPH?
I would say this is not a correct statement.  The main reason being that just because an enzyme is not a monooxygenase doesn't mean it doesn't require a regenerating system for NADPH.
Examples would be many dehydrogenase, hydroxylase and synthase enzymes. They also require NADPH regenerating systems to operate efficiently.  So, one of the CYP 450 enzymes may fall into any of these categories requiring NADPH/NADP yet not be a monooxygenase.