Hi Keresforth,  
It sounds like your cousin Michael is descended through the male line, so this would be fine.  The test would be on the Y chromosome, which is passed down from father to son ad infinitum (barring a few mutations along the way).  We would be most grateful if he would agree to test.  I will send you a private message with my email - would you be able to send me the genealogy that way?
Kind regards,
Carol