Tony,
Its not so much about removing the finish as it is cleaning the leather. Things like mr sheen and other silicone products settle on leather and you need to use cleaners to remove these - this is done to guarantee adhesion of colour. Cleaning with a strong solvent might also remove the finish, it doesn't matter wether it does or doesn't.
I have found its best to clean with two strong cleaners before applying colour.
1. Leather Prep: this is a storng solvent that will remove any silicones/waxes etc that are solvent soluable. It can also rmeove the leathers finish.
2. Alcohol Cleaner: this is an alcohol that will rmeove any water or alcohol soluable silicones. These are soemthing that a solvent may struggle to shift and vice versa.
Using a combination of the two products will make sure that the colour has the best chance of adhesion.
Now to address your question. You don't need to clean the full cushion, just the area surrounding the stain, and of course the sgtain itself. Its more than likely that the leather has a two tone finish with this type of damage, you'll need to clarify this. But assuming that it does, the best way to repair is.
1. Using the prep on a cloth wipe the colour from around the stain over the stain. This transfers some of the colour over the stained area blenidng it in better, and it rmeoves the edge from the stain.
2. Mix up a close colour or exact. Two tones are very forgiving and you don't always need to get the colour 100%. Then gently mist it over the stain to restore the colour.
You can look at duplicating the exact two tone appearance with colour application by sponge, but most of the time that isn't necessary.