TLDR: p.190 “Other Activity on Your Turn” - Communication gestures (flourish) can occur outside of your actions and moves. Opening your hand is a communication gesture that drops your weapon see “brief utterances and gestures” as you take your reaction to cast shield.
Since a reaction can be used on your turn, rules for what you can do on your turn actions likely apply in your special action-reaction on that same turn. It should follow that rules defined under the “Other activity on your turn” block should also apply on a reaction action taken on your turn.
Specifically, the section under the p.190 “Other Activity on Your Turn” block which define other activities as:
“Your turn can include a variety of flourishes that require neither
your action nor your move.”
This creates a short list of “flourishes” that are not actions or movement. The two flourishes listed are communicate through brief utterances, and communicate with gestures. p.190
“You can communicate however you are able, through brief utterances
and gestures, as you take your turn.”
The book then defines flourishes that are part of your move or action
“You can also interact with one object or feature of the environment
for free, during either your move or your action.”
The sidebar on p190 then provides a list of example interactions and the rules clearly state that a second interaction requires that you use your action. As stated by others, dropping a weapon is not listed there.
If brief utterances and gestures are available during your turn and outside of your move and action, then it is reasonable to infer that brief utterances and gestures may occur on another person’s turn as part of your reaction. A communicating gesture could be interpreted as the movement of your hand. For example, a gesture such as opening it briefly (thus dropping any held items). If you can move your hand as you make a melee attack as an opportunity attack reaction; moving your hand to make gestures as part of a somatic casting reaction such as one provided by the shield spell is logical.
Gestures are mentioned on p.201 under “Casting in Armor”,
“Because of the mental focus and precise gestures required for
spellcasting, you must be proficient with the armor you are wearing to
cast a spell.”
page 203 “Somatic”,
“Spellcasting gestures might include a forceful gesticulation or an
intricate set of gestures. If a spell requires a somatic component,
the caster must have free use of at least one hand to perform these
So to cast a reaction spell “Shield” that has a somatic component, you need “free use of at least one hand”, proficiency in worn armor, and assuming your hands are not grappled, part of “an intricate set of gestures” would logically include an opening hand gesture (thus dropping held items) as the first part of a “set of gestures”. Since (communication) gestures may occur outside of your move and your action, (communication) gestures (such as an open hand) should also be available outside of your reaction when it is taken to cast shield with brief verbal utterances and with a set of gestures.
If your DM rejects this argument, a simpler argument is that an open palm gesture (dropping held items) is the first part of the "set of intricate gestures" required by shield's somatic component as seen on page 203. Also thrusting an open palm at an opponent is a "forceful gesticulation" as seen on page 203 that has the added benefit of projecting a distracting weapon (+5 to AC please) that was in that hand at the creature attacking.
Anna from Arendelle can be seen using the open hand gesture as she
casts shield while uttering "No" in the movie "Frozen" which is clear by the shattering sword and her blue coloration that represents ice-like force magic.