Don't forget that the Danish are part of this, and they didn't exactly consider themselves German. Pan-Scandinavianism was also a thing at this time, arguably the Second Schleswig War putting the nail in it from Sweden's refusal to join with Denmark. However changing the flavor of German nationalism to include wider definition of who are 'German' would by nature change the Scandinavianism movement. A political movement that considers Denmark as somehow part of a 'Greater Germany' is a threat that would start causing butterflies by the Second Schleswig War.
Plus, let's not forget that Christian IX was not exactly a popular king at this time. He was a new king, and was dealing with the unjustified blowback from the loss. There's probably a reason he made the proposal in private, because its unlikely the parliament or people would have accepted it. He also clashed with the more liberal parts of Denmark by trying to prevent the spread of democracy. Even if Germany had agreed, I don't think the parliament or people would have just followed his decision. Denmark is no longer a country even by this point where a king can decide foreign policy by himself (It's likely the offer was only made in the first place so that if accepted, he could put it before parliament for a full accounting of their options). While an alt-Germany could use the offer as a reason for war in conquering Denmark, which it definitely could do, the rest of Europe would not allow that. Charles XV of Sweden had a claim on the throne of Denmark, and was a proponent of Scandinavianism. While Sweden failed to aid Denmark in the Second Schleswig War IOTL, a different form of German Nationalism would affect Scandinavian nationalism. Not to mention Sweden would be far, far more likely to declare war to prevent Germany from taking the Sound and save Denmark than it would to help Denmark keep its German fiefs, and the Danes would be far more likely to embrace embrace a policy of Scandinavianism and accept Charles as their rescuer than they would to accept an unpopular king's decision to put Denmark in the German Nationalism movement. Great Britain does not want Germany controlling such a vital naval position as the Sound, and OTL already showed France would use imbalances in the Great Power to attack Germany.
I see no way Denmark could have been annexed in OTL without an alt-Great War. The Danes would almost certainly rebel against Christian IX, and likely by that basis either declare a Republic or if Sweden decides it doesn't want the Germans right across the Sound from them and declares war on the side of the Danes might choose Charles as king. Germany either accepts this and pulls out, or decides to use its army to its advantage. However the Prussians and Austrians likely wouldn't cooperate long term, and Great Britain and France would likely get involved by this point. So this likely ends up with major fighting, and Germany probably, probably, loses. Denmark either is a republic or absorbed into a Scandinavian Union under Charles.
Now its been discussed that an alternate form of German Nationalism would probably be needed, and I agree, but thus form of German Nationalism would almost certainly require to somehow make Scandinavianism nationalism a subset of German nationalism. Otherwise you probably aren't going to get the Danes to agree, and Sweden is already very neutral but can be pushed if Germany is conquering Denmark. You'd also need to the balance of power to be preserved as to not prevent every Great power from jumping to prevent a Greater Germany from forming. I'd say the political situation of Skallagrim's #2 option would indeed be the best chance of achieving this. A Northern Germany with Denmark might be tolerated if the other powers were convinced they could play Northern Germany against Hasburg Southern Germany. I agree that the #1 option just isn't likely to be tolerated without a Great War breaking out with this Germany likely against Great Britain, France, and probably Sweden-Denmark.
A lot of times during negotiations these tentative sort of offers were extended not so much by them being realistic or possible, but just to sound out the other side. In this case, it would likely Christian checking if there was any possibility of the Germans allowing Denmark to retain at least some control over Schleswig-Holstein. Once the offer was refused, it was a clear sign that they wouldn't allow it. I think that's what this was. Not a genuine offer but a negotiating tactic to check the mood of the victorious Germans.