personaly i would upgrade to 1903's latest version first and check if everything is working. (or 1909 when there are a bunch of patches out, when you aren't in the mood for early adopter)
i'm not recommending 1907, since we have heavy trouble with a not working tunnel, and searching the forum, we aren't the only ones.
after upgrading to one of the 190x release i would move with the same version to the new server.
moving and upgrading at the same time is something i won't consider. when you run into problems you'll have a hard time if it's because of the move or the new ws1 version.
9.6.x is fine to just upgrade in one step