Your water bottle example doesn’t apply, as it involves shear between the fluid and the container walls. The water in a watermelon is contained within cell walls, preventing the shear-mixing you describe. Your bottle would also exhibit mixing due to convection, another effect the watermelon can’t access.
Dropping a watermelon also doesn’t apply; it’s easy to induce mixing and flesh-tearing if you rupture the exterior walls, but that’s already been disallowed by the OP.
The fact that this is all water means it’s hard to tear the flesh internally. It’s all hydrostatic, so you can’t easily create large pressure differentials across the flesh (aside from sound waves). The cell structure may be weak, but it’s supported by the fluid pressure of the cells adjacent to it. It’s watermelon cells all the way down, as it were.
And focused ultrasonic waves might do the trick, as would an underwater explosion adjacent to an underwater melon. But I’d be surprised if a paint shaker could tear apart the inner flesh without first tearing apart the outer flesh. If watermelons had voids or dense pits, though, I’d be right there with you.
If you think I’m wrong—and of course, I might be—you’re welcome to sneak a watermelon into Home Depot. All I ask is that you post a video of the aftermath, whether that involves an internally liquefied melon, store security or both.
Here’s a thought: freeze the watermelon and then thaw it.
One reason it’s hard to preserve living beings by freezing (if you also want to keep them living upon defrosting) is that the ice crystals rupture cell walls. We want ruptured cell walls in this case, so maybe freezing would do the trick, at least partly.
I have no idea whether the rind would rupture as the volume increased, but maybe it wouldn’t.
There are lots of ways to destroy a watermelon, but I was hoping to use the force of the flesh itself.
The sound idea seems like it would work and is pretty close to keeping with the spirit of the OP. Also, the seeds may provide the ball bearings, and since they’re inherent to the melon, I think it counts.