I would use OSC to change the video cue playback rate incrementally; this could be done with Network cues with hotkey triggers or from StreamDeck / Companion. If you make the increments small enough you'll have good control and shouldn't be noticeable to the audience.
to increase the playback rate
/cue/{cue num}/rate/+ 0.2
to decrease the playback rate
/cue/{cue num}/rate/- 0.2
If you number all your kayak lyrics cues K1, K2 then you could use
/cue/K*/rate/+ 0.2
providing you remember to reset the rate before starting the next song lyrics video
/cue/K*/rate 1
hope this helps