What would result if these two married does Hanover still get annexed in 1866 by Prussia or would Britain absorb somehow?
A more overtly pro-Prussian position in Britain means Denmark is even more pissed off to have been 'thrown to the wolves' by the British after two decades of promises flowing out of London ensuring British support for the Danish position over the Schleswig-Holstein Question. This might be enough to shift Danish popular opinion and governmental policy away from their IOTL fade away into obscurity & neutrality and possibly into a pro-French orbit.
These were the views of the royal family, not of the liveries. Denmark would've been thrown to the wolves anyways. I can't see the government of the day acting any different despite household differences.