I'm not sure about the procedures for using a private courier firm. The CN22 and CN23 forms are recognized throughout the world because they're approved by the Universal Postal Union. If you're sending goods through a non-UPU system, there might be different requirements.
The courier should be able to advise you of the relevant requirements. (Check their website for either direct information or for a helpline phone number). If they can't provide the information, you'd probably best be advised to avoid them anyway.
As a starting point, here's the link to UPS's webpage about export documentation:
http://www.ups.com/content/gb/en/resources/pre pare/documents/export/index.html?WT.svl=SubNav
(Check the links down the left, including ' commercial invoice' for further information).
Chris