Newfoundlanders have been known to take a song and change the lyrics. Then they change the tune and add completely different lyrics and so on until the work is completely unrecognizable. Relax, I'm only joking.
Give credit where it's due and take credit for your own interpretation. A simple "Arranged and Adapted by... " should suffice.
SOCAN (the music mafia) would have you scared to whistle a tune on in an empty bus shelter.