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So, I decided to make a recording of my humming what I remember (including the sh-shook) part. https://vocaroo.com/11KWPTVHO6Y6
the parts where I go "duhduhduhduh" were actual words in the song, I just don't remember any of them.
What region/territory have you heard this song in? Mainstream is a YMMV concept — which itself is a YMMV statement. It may be possible to find it in Top Charts of that decade, just want to know the region/territory since they could differ. Prisencolinensinainciusol, for instance, was very popular in Europe, not so much in English language territories though.
AFK with issues, will returnWhen I read your comment, I at once remembered Sugar Town by Nancy Sinatra. Maybe some male singer covered it.
Edited by Kisujj

This song from The '90s that was on the radio a lot.Male singer, genre maybe rock? The main think I remember is in the chorus someone says the "word" "shu-shook" repeatedly. The rest of the chorus (and the song in general) was real words, but I can't remember any to look up