This is possible since Kashubian is more distant to Polish than the Lesser Polish Dialects and Silesian.
Here is the problem with that. Throughout the Free City's existence, the non-German locals identified themselves as Poles and would prefer to join Poland. Once Gdansk's Germans are expelled, the only option left that was realized IOTL is as a normal collection of municipalities in the People's Republic of (aka Communist) Poland. Any representation of a Cassubian/Kashubian identity was very minor during the Free City's existence and was suppressed under Communism, in which case linguistics took a back seat and politics took center stage since the locals and Polish officials at the time saw themselves as speaking a dialect of Polish (even if, to be sure, it was divergent from the literary standard). From this POV, whether or not it was true, "Pomerania" is a German imposition that needed to be expunged from any conception of postwar Poland, and hence no mention should be made of it except in a negative sense, wound up in the Sovietized concept of Western betrayal and all that. So any expression of a separate Kashubian identity post-1945 is not feasible, nor for that matter any annexation of what would become part of East Germany.
However, having said that, -
if we alter the course of WW2 to allow the Free City to continue, even with the expulsion of the German population, we could twist it around due to the question of which Poland to transfer Gdansk to. After all, the creation of the People's Republic was pretty shady indeed, so in that case it would be as a Finlandized Hong Kong type of state that could allow the Free City of Gdansk to continue in a Trieste type of arrangement. That could probably work, but how to get to that point I don't know. Thus the Government in Exile could be restored AND we'd get a local take on Polish national identity.