Don't know about the 1860's but according to the wiki article below they were by 1900.
BTW what prompted the question?
It's very possible though. The American kepi was modeled on the French version (even the word is French, meaning "small cap" ) so why not the Greek army?
http://en.wikipedia.org/wiki/Kepi
Always wondered why the dang impractical things became so popular. They are next to worthless in the sun and absolutely so in the rain. Many western troops in the WBTS on both sides threw them away and acquired a civilian slouch hat.
BTW history DOES repeat its self. Just after the National Guard adopted the black beret a few years ago I heard a long time soldier complaining about them. I told him the US army has a long history of issuing worthless head gear!