Okay, I wrote a batch file that will check the current status of DDraw.
If DDraw is on, it will turn it off and start JK, then wait until you finished playing playing and re-enable DDraw again.
Should you start this while DDraw is off for any reason, it will just turn DDraw on and exit.
http://www.mediafire.com/?a8ip5f42iv8tio4
Drop the file into your game folder and doubleclick to start it.
I tested this on winXP and it works fine here, but no guarantees.
EDIT: While this works in running the cutscenes without corruption, there's a minor problem: The game won't have hardware acceleration available without ddraw, so it's more or less unplayable... :/