We'll to answer your question there have been a few declared wars with no casualties but in spirit they are closer to international incidents. An example of this is the Anglo Swedish war 1810-1812 where no shots were fired no combatants sent to fight. Others had nations send troops but no shots fired like the Pig War of 1859 which had no casualties. That was nearly a war but cooler heads prevailed and the British realised how stupid it would be to fight a war with the USA over a pig. Now I can give you a major battle with no casualties where both sides were trying to kill each other The Battle of Fort Sumter that opened the American Civil War was a battle with no injuries. Another example of battles with no injuries are the first battles of the Flagstaff War were the only thing destroyed was a flagpole. The final piece of bloodless war that I can give is a bit of a joke answer which is the Emu war of the 1930s mentioned here http://trove.nla.gov.au/ndp/del/article/4508317
I am usually proud to be a Buckeye. The State of Ohio has produced presidents, astronauts, and scientists. It also features a rich martial history, and has produced many generals, crushing victories, and ace pilots.
Then we get to the Toledo War. Michigan was attempting to become a state in 1835, it claimed a strip of land that included the city of Toledo. Ohio wouldn't stand for such a loss of territory (though its ownership was disputed, to be fair to those folks up north). So, the respective territories mustered up militia units and shipped them off to war. The Toledo War, or Michigan-Ohio war was the result.
Both units wandered the wilderness. Blood was spilled. Michigan units tried to arrest some Ohioans, including Major Benjamin Stickney. His son, Two, stabbed a Michigander with a pen knife. Yes, the son's name was Two. The other son's name? You guessed it. One. Seriously. The guy he stabbed was fine, but he technically did bleed, so "blood was spilled." The lone military "battle" saw the two militia units finally finding each other, taking up positions on opposite sides of a river...then firing into the air and running away from each other.
There was a political settlement. Ohio got to keep Toledo and the strip of land it was on. Michigan got the Upper Peninsula.
Nobody died, a man with an embarrassing name did technically draw blood, and the whole thing ended peacefully. Thus is the story of the "Toledo War."
I'm going back to thinking of famous Buckeyes and their military triumphs. Eddie Rickenbacker's exploits in WWI, Sherman's March to the Sea...ah, there, I feel better about being a Buckeye again.
Sorry, but we don't allow throughout history questions.