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"You may now always perform the Somatic Components; Weapons and Shields are enumerated because they are notable

"You may now always perform the Somatic Components; Weapons and Shields are enumerated because they are notable"

#Conclusion

A non-weapon object used as an Improvised Weapon only counts as a Weapon while the attack is being made, and afterwards, mechanically, it is no longer a Weapon. So when a spell is being cast, it would not count as a Weapon.

#Conclusion

So under these conditions, you would not be able to cast the spell Shield.

So under the conditions of

• being a spellcaster
• with the War Caster feat
• that is holding two objects
• one in each hand
• neither of which is a Weapon or Shield

You would not be able to cast the spell Shield, which itself lacks Material components—hence why the Wand doesn't satisfy the "Somatic Components may be performed while holding a focus if the spell has Material components).