Any way to add (primitive) dynamic music?

I want to implement a primitive version of a "dynamic music" system into my game. Basically, one track would play and then the game would start a different track when the player clicks on a link, but I want the second track track to "line up" instead of just abruptly playing.
My idea is to play multiple tracks from the start, with all but one being muted. Then when a link is clicked, a different track is unmuted and the first one is muted, so they're effectively "switched out".
I tried this on Scratch before, and it mostly worked except for some lag caused by, well, Scratch being Scratch.
Anyway, I'd like to know how to do this using Squiffy. I imagine my method might also be laggy, though, due to the multiple songs playing at once. If you guys have a better idea then please let me know.

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