Nevr Dull is a wadding (believe it is cotton gauze) that is treated with chemicals and sold in a can. I have used it on many metals but don't personally care for it on my silver.
http://www.nevrdull.com/I personally like Wrights or Goddards silver cream. It does take a rubbing time...but the results are gorgeous!
Love your piece. The handle is exquisite. I am a big collector of silver pieces....and this one is an older one. It is apparent it has been well used....appears that the silver plating has been worn on the blade and looks as if there is a little bit of pitting in the handle. Would be interested if you had it tested if the handle is sterling or plate? Silver dulls/tarnishes from exposure over time......lets see it after you polish. (The best polish for silver is USE IT!!! Don't just store it away!)
I would not advise any harsh chemicals since you already have some plate loss on the piece.