Smaller doses of iodine will help and is safer than taking large or concentrated doses of iodine. And you will get the other benefits of the herbs containing the iodine. For example seaweeds support the rest of the endocrine system, build the flora, boost the immune system, etc. Taking a product like Lugol's will not produce all these benefits.
Good sources of iodine include seaweeds, watercress, black walnut hull and nettle leaf.
I have never heard of chlorine depositing in the body. Fluoride will though.