Reducing box volume - best material

A little give may or may not be a problem, I'd be a bit more concerned it didn't resonate but again it depends, for example a high frequency resonance would get some damping from the stuffing around the object anyway. A larger bottle of water may be subject to some modal stretching but smaller ones may be less of a concern.
 
I have not found any cons for going with used stuffed animals.
 

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That may actually increase the volume seen by woofer. Seriously, thats what stuffing does. Even if that stuffing looks like cute animals. 🙂
I would use gold bars. Its durable, heavy, does not loose value. No issue as i see it.
You can push the vice to put diamonds bag inside if the loudspeakers has diamond tweeters. I had good result with a neighboor in an Onken one day.

But more seriously, sand is easy to weigth and take volume in a plastic bag... Perhaps a good idea to put a geometric standind wood bracing as well, but less easy to tune and measure the volume when assembled. One stone, two birds (not in the loudspeaker I mean)
 
If you can, choose something that achieves a dual purpose. So as well as reducing box volume, choose something that might brace the cabinet, or add bitumen-like damping to cabinet walls or add another layer of wood to increase wall thickness, perhaps glued or perhaps via CLD (constrained layer damping) or add something that might help to break up the rear wave, etc., etc.