I think it's fair that I actually propose what, IMHO, is a likely series of events in case of war.
1. The American intervention affects the situation in Venezuela not one iota. No coaling bases nearby, smaller fleet than the RN's Flying Squadron that can coal at Trinidad or Barbados. The American fleet stays home. American commerce is paralyzed, British commerce delayed, but doesn't experience much more than the occasional hiccup required when rumors of American warships crop up. Big business in New England and the Mid-Atlantic is furious with Cleveland. A couple American detachments on land prepare themselves, possibly execute minor raids barely worth mentioning.
2. If war persists for more than a month or so, the Flying Squadron and a small contingent from Britain numbering about 10,000 men concentrate at the very well-fortified harbor at Bermuda. Panic on the East Coast ensues, to a far greater extent than in OTL's Spanish-American War. Light-to-no action in the Pacific, as the British Pacific Squadron at Esquimalt and the American Pacific Station are relatively evenly-matched. Anyone's guess as to whether the slightly-outnumbered US Asiatic Squadron runs home, runs around China doing little damage, or gets caught and pounded by the British China Squadron.
3. If the Southern Democrats don't want to fight the war, Cleveland's adventure ends. Britain would be well-advised to make a brief descent upon a port in the South such as Charleston, which has very simple SLOC with Bermuda, with the added possibility of drawing out the American North Atlantic Squadron and defeating it.
4. The British Flying Squadron with small attachments of cruisers from the North American and West Indies Station and perhaps a few others that can be scrounged up fight a pitched battle against the American fleet, which they outnumber by a small margin. Both fleets' capital units consist of brand-new or recently-commissioned vessels, so expect some of the worst shooting in history. I give the probabilities of British victory-Draw-American victory as roughly 30-50-20. A draw works for the RN as well as a victory, as the raid and capture/destruction of Charleston will still go forward.
5. Assuming RN victory or draw, no one in America is interested in fighting anymore, especially when the pro-business Republicans sweep into office at the end of 1896. America sues for peace, pays indemnity of a tolerably low amount (probably that for destruction of any British materiel), the end.
6. America is slightly less buddy-buddy with Britain over the next two decades, but not overly so. American entry into WW1 takes place at roughly the same time.
In other words, a short, simple war is to be expected, interesting for naval historians perhaps, but little else.