Pretty clever. I wonder if the cotton will reduce the flow too much once it's wet and the fibers cling together. If it does, you could try adapting the fine mesh screen that's found in the aerator of a sink fixture. It might even be the right size.

The aquarium pump definitely has possibilities if it has enough capacity. That's kind of what the MSR Trailshot is like. Of course, there again, you'd be adding a few ounces. You'd need some tubing, too. The food grade silicone tubing is nicer than the polyethylene (and more expensive). I got some to replace the hoses on my PUR filter here:

https://www.freshwatersystems.com/