If it's not covered under the policy, then expensing it would be dishonest and petty theft. It's yours. If the company ever starts looking for a reason to fire you, you've given them one.

I bought a pair of tiny $10 umbrellas by Totes for Mrs BamaVol and I. They can't be any longer than 6". I keep mine in my computer case which means it travels with me although I may not always have access to it when the rain starts.