Chechnya is not a Russian province. Chechnya is a Republic within the Russian Federation. I think a better analogy would be to Scotland, Wales or NI in Britain.
Not sure what your trying to say here, though the slang the Russian troops used is literally “Czechs”, as well as a few others like “cherniye” (blacks). They were not shortening the word “Chechen” to “Chech”.
Not sure if you saw this, maybe it’s of interest:
Also, it’s worth noting that this guy was a major figure in the Chechen conflicts and he is originally a Saudi:
http://en.wikipedia.org/wiki/Ibn_al-Khattab