Given that the song first appeared in 1877, I think it is much more likely that it was inspired not by the Crimean War, a generation earlier, but by the fact that in that year there was a war between Russia and Turkey,arising out of an uprising in Bulgaria. The press would have been full of it at the time, stories of atrocities and all.

What sem to clinch it is that the song specifically mentions the Danube, which is a long way from the Crimea, but became the Northern border of the principality of Bulgaria which was established in that war.