I don't think it should be that complicated(as a vague concept of how, I don't know how to script). Make the spells you learn(or some of them, like non-concentration destruction, at least from vanilla and DLCs) also give you a lesser power, that costs as much magicka as the spell itself, which makes your next phisical hit apply, besides the normal damage, the effect of the spell(even AOE), be it with an arrow, bolt, one handed swing, shield bash, or two-handed swing(maybe even unarmed, but I think that would be even harder). That way you can apply magic to phisical attacks even with both hands occupied. But take note that for melee it would be best to, if possible, make a different area shape(cone instead of radius, for example). The script could be activated retroactively by completing a quest to learn "the art of spell binding" or something like that. The powers could also be to prepare other unrealistic uses of weapons, like multi-arrow, arrow rain, charge, teleporting behind the target and backstabbing, flying slashes, slamming the ground with your warhammer to stun or knockback enemies, etc.