I don't see how he can. 'Prince' is a title Andrew was born with and cannot be 'taken away' by any individual. Likewise, his titles were gifted by the Queen or were conferred owing to his naval retirement package, lodge membership, Letters of Patent, etc. Only an Act of Parliament can formally strip his legally-entitled statuses. I suspect what has really happened is that the titles have simply been put into abeyance, to appease perceived public anti-monarchy feelings. Rather like 'Ginge and Cringe' being told not to use their HRH title.