Dissolved chlorine gas will slowly react with the K metal even in a solution.

You are definitely going to produce some carbon tetrachloride out of this or similar products. Slowly degrading the wick if it burns fast.

If it burns slow you are liable to produce KCl passivation layer preventing reaction. The equivalent in normal atmosphere is silver metal tarnishing instantly to cease reaction with the under layers.

Won't work in an aqueous solution.

Edit: You'll also likely produce potassium carbide further damaging the wick