Something I've thought about as of late with this is the possibility of it having a more immediate effect on events elsewhere, rather than the gradual butterfly effect I suggested earlier that only hits those directly impacted.
For example, there was an Anglo-Russian near stand off concerning the Danubian states of Wallachia and Moldova in 1848-1849. The Russians had occupied them, in concert with the Ottomans initially, to put down revolts but it appeared the Russians might seek to either annex them or bring them into their own sphere from the Ottoman one. London was apprehensive over this, and threatened to send the fleet and the Russians made clear this would engender war. Ultimately, the British backed down and the Russians peacefully resolved it with the Ottomans. If the UK is distracted by events in North America, in terms of seeing the need to organize Canada and the like in light of the events South of it, could Moscow use that as leverage or trick itself into perceiving the British as being too distracted? If so, we'd likely get a Crimean War in 1849, but without the French and Italian contingents to back up the Anglo-Ottomans. How that goes is hard to say, but the advantage does seem to be in favor of the Russians.
This also produces other effects. Without the Russian intervention, it's likely the Hungarians can force the Austrians to a diplomatic agreement in their ongoing conflict; an earlier Ausgleich perhaps? In the long term, this would be great for Austro-Hungary in terms of helping to solidify their internal conditions, perhaps also ironically checking the Hungarian nobility that proved troublesome historically. In the short term, however, the new state is going to be too focused domestically to do much in its abroad. Does that mean the Italians might win their quest for independence? Does Prussia successfully enforce the Erfurt Union to create the German Empire in 1850?
Depending on how you're willing to stretch the butterfly effect, much can happen.