Doesn't sound like a dumb question to me! Sounds like a pretty great idea!
I would think that would be fine enough for the Purigen beads... it has to be a really fine mesh or yeah... you end up with a mess.
Only issue I can possible see is if you want to regenerate it without taking it out of the stocking. Not sure what bleach will do to the material - if it'd just eat it away, or degrade it enough to cause it to burst the next time you put it in your cannister. Might want to do a test run with an empty stocking in a 1:1 bleach/water solution to see what happens...
Let us know!