One possible example is the Ecuador-Peru war of 1941. Were there others?
Just to be narrow/precise, restrict attention to any wars that were ongoing any time between Sep 1 1939 and May 9 1945.
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Initially the Winter War between the USSR and Finland was an unrelated conflict, as neither of the two belligerents were involved in WWII when the fighting broke out. However, it was still going on when Germany invaded the USSR, at which point Finland found themselves allied with the Nazis.
You could make a case that the Second Sino-Japanese war was also unconnected, as it started far before the official start of WWII. However, many (particularly on the American side) will instead argue that this war was the first action of WWII.
Outside of those, you will have trouble simply because every other region of the world was dominated by the European Imperial systems, and thus got dragged into WWII when their European masters did. The sole exception is the Americas, where I believe the Ecuador-Peru war you mention was the only other conflict to occur during this period.
Although the Spanish civil war does historically predate the Second World War, many of the participants, particularly Germany, used the Civil war as a training ground for their Army and Air force.
The Spanish Civil war refugees in France were affected by France's fall to Germany, in that they were shipped to Nazi concentration camps.
Wikipedia does also mention that there was guerrilla warfare in Spain until the 1950's.