I have always heard betadine/water soaks in a weak tea colored solution and no polysporin for that exact reason.
That chlorhexadine glutamate 4% seems like maaaaybe not such a good idea. I just read up on it and while it is indicated that it is used for cats and dogs sometimes and is better than saline (which I don't think is saying much, really), depending on the concentration (per Wikipedia) "At low concentrations of chlorhexidine, this results in a bacteriostatic effect; at high concentrations, membrane disruption results in cell death." Maybe the concentration is too high?
Anyone else have a thought?