@ chocotwix
The letter explaining is your letter to the cic no need for company letterhead. You will state there the nature of your work, plus terms and conditions of your employmet that are not stated in the documents you got from the company.Explain mo din why the hrd refused to issue the information you need like as per their policy etc...If you can secure another document that the hrd does not issue a document stating your annual compensation, number of hours etc., the better.
So the letter should be signed by you.