There are some shield you really could just drop out of your hand easily but there are many others that were strapped to your arm. So it seems like D&D takes the safe route that all shields need to be doffed with an action to be on the safe side.
Though even if you could do this via the rules I'd still say no. Yes, 5e works as if simultaneous events were happening sequentially but I, as a DM, would say you can't simultaneously wield and not wield a shield at the same time.
Though even if you could do this via the rules I'd still say no. Yes, 5e works as if simultaneous events were happening sequentially but I, as a DM, would say you can't simultaneously wield and not wield a shield at the same time.