I'm having a bit of trouble reading/understanding your question.
What do you mean by "the kit"? Could you link to the sort of kit you are talking about?
You are almost certainly not going to be able to integrate a music box into an existing pocket watch without ripping out the guts of the time mechanism. Even if it's a quartz mechanism that leaves out all the springs and gears, whatever space you'd have to work with would still be cramped and awkward.
Assuming you don't mind the watch face being merely decorative, it would not be out of the question to handmake a custom musicbox mechanism by hand entirely from scratch. In the 18th century, both mechanical pocketwatches and music boxes were made using few tools beyond a jeweler's saw (less than $10) a set of needle files, and a soldering iron (which was literally a hunk of iron heated in the fire). The only really hard part is the gears, and there are tricks to handmaking those.
Personally, I wouldn't want to start on such a tiny and awkward shaped music box, but even in modern times, people have started off handmaking similarly small devices.
You mention getting a disk made. Because the comb needs to be perpendicular to the indentations on the music box media, you'd probably need to make a cylinder type music box, not a disk.
One thing to keep in mind is the volume of such a prop. The key to an acoustic instrument's volume is the transmission of vibrations to an appropriately sized resonator. The space for a resonating cavity in your pocket watch is going to be tiny, so the volume will also be tiny. In a big echoy convention center with plenty of people in it, no one will be able to hear the music without holding the watch right up to their ear.
Anyway, if interested in making a music box yourself, I can point you to resources.