It's surprisingly easy, if Gustau arrange a marriage between his daughter and Christian 4's third son Ulrich, Christian would bend backward to keep the Swedes happy. Another alternative could be if Gustau's wife died, and he became engaged to one of Christian's daugthers, as these daugthers was of questionable legitimacy (as their mother was high noble not royalty), the marriage of one of them and the Swedish king would remove these doubts, making them all potential marriage partners for other European monarchs, and as such strengthen Christian's diplomatic position. As for the Swedes, it wouldn't be the first time a Vasa had married a high noble, so for the Swedes it would be less of a big deal.