To be sure, shmel'chik or shmyel'chik (шмельчик) is a Russian word, and still in use for big bumblebees and for male persons, though not mentioned in dictionaries. From the texts I googled, I could not deduce the meaning for persons either.

My wild guess is that shmel'chik here refers to a man who persistently woos or pesters a young woman - similarly to the Italian word "pappagallo" (= parrot). The fictional urban Olga may have had a swarm of such wooers - whereas a muzhik (= boorish person) belongs to a different sphere. Sado-masochism requires a certain level of style.

The author of the song seemed to address an audience who knew those Russian words, presumably from some popular English novels, plays, or films of that time. It is such fashions - rather than the clichés themselves - that lend themselves to good parodistic comedy.