According to Anna Sophia of Prussia, duchess of Mecklenburg's wiki, it mentions that:
Since Duke Albert [of Prussia] had no surviving sons of his own, he attempted several times, unsuccessfully, to make John Albert I [of Mecklenburg] his heir and successor in the Duchy of Prussia.
So, simply marry Anna Sophia to a Vasa prince and off we go. Sweden would have the sort of army/cash Mecklenburg would not in order to seize the duchy of Prussia by force.
Another option of course would be to marry Elisabeth of Prussia (Albert's uterine sister) to Carl IX of Sweden. And then cement the alliance by marrying Albert's eldest daughter (Anna) to Carl-Elisabeth's eldest son. Ironically, Anna would also be one of the heirs of Julich-Kleve-Berg through her mother. A Swedish Rhineland would definitely be interesting.