I would imagine that the butterflies would be more minimalist in the short term.
The key for this is not that the outcome changes, but the people who brought about the outcome do. In this timeline, the final defeat of Napoleon will be seen as a continental, central/eastern european triumph, not a British one. As such, the axis of diplomatic power will shift to Austria, Russia, and Prussia more than in OTL.
Especially if this what-if involves a defeat of Wellington, you will see a reorientation of British strategic priorities. In the short term, this timeline's britain will care far less for the army and european politics. The army will be firmly relegated as the junior service more than in OTL, as it will have been the navy which brought home triumph after triumph (it got to the point where Calder was court-martialed for Cape Finisterre), while the army has only minor victorys to remember (Penninsular campaign will not be remembered nearly as brightly in Britain), and no true heros (wellington and company having gone down in flames at Waterloo). As such, Britain will detach herself more from continental affairs (example: no involvement in a Crimea style conflict) in favour of the Empire.
One interesting long term effect is this may push France and britain closer together. In this timeline, the eastern members of the coalition, Russia, Prussia, and Austria, will enjoy most of the spoils. Given historic rivalries, it is unlikely that this coalition will remain together for long. However, from a British point of view, this alliance must be removed as soon as possible. For centuries, british foreign policy has been to prevent one power from dominating the continent. Once the threat of Napoleon is seen as finally gone, Britain will do all in it;s power to break apart the old coalition in it's favour. One aspect of that that we might see is Britain backing france to a greater extent as a counterweight to the powers of Austria, Prussia, or Russia. This historic reversal may well happen far earlier than it did in our timeline, and would have interesting repercussions.