I'm not familiar with corrosionx, but if it will remove rust staining it will remove bluing (which is another oxide surface just like rust).
That looks like one of the models with a "raw" hammer sides but the edges are blued.
Looks to me like there is just enough pitting to keep it from cleaning up with just steel wool.
To clean that up, you will need to remove the hammer from the frame. No problem there...a simple job that is outlined in the owners manual.
https://ruger-docs.s3.amazonaws.com/_manuals/blackhawk.pdf
You need:
-A couple sheets of wet-or-dry sandpaper (400 or 600 grit).
-A flat surface to use as a working surface. (a glass kitchen cutting board works great and is about the perfect size, but any good flat piece of glass will work)
-a bit of water
-your choice of gun oil
-Paste type floor wax to help seal the metal afterwards (optional)
Remove the hammer from the pistol.
-Take a sheet of wetordry and lay it on the glass surfacing block and wet it down with a little water.
-Lay the hammer on the paper and using very light pressure sand with a straight line motion in the same direction as the existing marks. Check your progress frequently...you don't want to remove too much metal, just enough to clean up that pitting and haze.
-Repeat for the other side of the hammer if needed.
-Wash the part in hot soapy water to remove any stray grit and dry well. Pay attention to the sear notches...you don't want to leave some grit in there and give the pistol an unintentional trigger job.
-You can either finish the job with a coating of oil, but I prefer to use paste type floor wax to seal the metal. It's not a permanent seal but is tougher than just a thin coat of oil.
Reassemble and be more cautious about where it gets stored the next time.
