I went RN to RAF 7 years ago, on leaving RN the only letter I got was one pointing out that I wasn't allowed to wear the uniform anymore, just as well really as the bits I did not give away it went on ebay.
Turned up in the office wearing a jumper with no wings and Flt Cdr was quite shocked as I could be mistaken for a blunty, when asked which ones I should wear we decided on RAF as that was who I work for now and the Navy ones would look silly on an RAF uniform, sensible decision.
I do now have a couple name badges with RN and RAF wings but that works well where I work is truly tri service.
Frankly this all seems a lot of fuss about nothing, you wear the uniform of the service you work for, if you are really that hung up about wearing the wings you earned in training why are you leaving in the first place?