Can I hide my master degree permanently?
Hide it from whom? The only scenario I can see is that you want to omit it from your CV. But if you do that, how are you going to explain the one year gap?

It's also worth noting that you didn't get "a first class honour in the BA". You may have got first class honours in one or more years of the Tripos, but your degree certificate will say merely that on a certain date, in a congregation holden (sic) in the Senate House, you were admitted to the degree of Bachelor of Arts. Not that my employers have asked to see the certificate.

Finally, "permanently"? Don't make rash decisions which you might regret. In two years you'll be able to graduate MA and that (in Cambridge terms, at least) is a higher degree than the MMath/MEng/etc. You can put MA (Cantab) as your postnominal letters on your CV and hide the Mxxx that way, although it will still make sense to mention it as an explanation for what you were doing this past year.