this is not from a pro but (that never stopped me before)
I would suggest applying over Denshield would be fine. I believe the proper adhesive would be based upon the material you are applying which, in this case, is the vinyl so the adhesive supplied with the tub surround would be proper.
Just as support for this, on the job I am currently working on,( a 600,000+ sq ft hospital) Densshield was installed in a lot of places. Some places have back and side splashes for the sinks made from Corianne. These were installed using PL something (can't remember, seems like 200 but could have been 700). FRL (basically plastic laminate sheets) were also installed using the same adhesive. The FRL would be a similar installation to what you are doing although they are not in the shower area. I do not believe that would make any difference though.
Caulk any edges to prevent water infiltration behind the overlay.
I would NOT use thinset as thinset is designed to be used under (or behind) a very hard rigid surface. It is not flexible so the flexibility of the laminate on the board (the board will give and flex to some extent) would most likely result in failure of the thinset.