(a) The Mayor is hereby given the option of issuing one license to cover all solicitors who, without compensation or remuneration, solicit only in behalf of and for any locally or publicly recognized religious, educational, civic or other charitable organization, instead of requiring an individual license for each solicitor.
(b) Where a general license is issued for one organization instead of an individual license for each solicitor, such organization may be required by the Mayor to issue to each such solicitor doing business in the city a written and uniform authorization and identification in such form as shall be satisfactory to the Mayor. Each such solicitor shall have such written authorization with him or her at all times while exercising his or her calling, and shall exhibit it to any police officer or city official upon demand.