I think the Danish scenario is rather farfetched. Assuming Sophie is out of the question because she's already Grand Duchess of Saxe-Weimar (as consort to the Grand Duke), she still has descendants who could do the job. Barring her son who is heir to Saxe-Weimar and his two minor children, the obvious candidate is Sophie's daughter Marie, married to one of the countless Heinrichs of the Reuss family. I can't help but wonder if a Dutch Reuss family would have continued the tradition of naming every male member Henry (in this case, probably Hendrik)...
However, assuming Sophie does take the throne, I'd guess she's more likely to be succeeded by her grandson Bernhard, who in OTL died at the age of 22 in 1900. However, I'd guess that his death may be butterflied away.
Another factor to take into consideration, is that a Wil(h/l)e(l)m Ernst who is raised from the 1880s on with the prospect that he's the logical heir to the Dutch throne, might have an entirely different attitude towards this inheritance than the WE of our timeline. One would think that the Dutch royal throne is more prestigious than a 'mere' German grand duchy. So perhaps he would want to succeed as Willem IV, and leave Weimar to his younger brother.
I doubt the king/queen, whoever it will be, will 'reign' that much different than OTL's Emma and Wilhelmina. After all, although Willem III liked occasionally to explore the limits of his constitutional rule, his political role was still very limited. If Sophie ends up queen, she might also be a half-absentee monarch, spending half of her time with her husband in Weimar, which might even speed up the process of reducing the monarch's role.
, a question that is more interesting than the one who would become king or queen, is what this does to the monarchy's popularity. As it has been pointed out, the three Willems (and the last one in particular) were never very popular, and some German foreigner will probably be even less welcomed, despite the Weimars reportedly all knowing Dutch. The Wilhelm Ernst of OTL was particularly unpopular in his own Weimar... In OTL, it's queen Emma who has been credited with 'reinventing' the royal family and boosting its popularity. I don't know, however, how much of this is due to her as a person and how much to having good advisors.
Also, the tradition of koninginnedag was originally invented as a celebration of (Princess) Wilhelmina's birthday; without a Wilhelmina, this would not exist.