What you suggest "might" work. But in my experience does not long term.
Skunk smell, for example, is oil based.
Baking Soda and Hydrogen Peroxide can be used to 'neutralize' skunk oils but does nothing to remove them. Dishwashing liquid will, indeed, 'emulsify' skunk oil, and the hydrogen peroxide and baking soda 'neutralize' it....But it doesn't really 'remove' it.
A better type product is "OdorMute" which is a bacteria culture that feeds on animla oils.
Once applied, the bacteria culture begins to 'feed' on the skunk oil biologically transforming it into a form that no longer 'smells' nor any longer remains in an 'oil' solution...