Yes, Flitz will fit the bill. CAUTION: do NOT use any power tools. Use an old 100% cotton T shirt and use the Flitz by hand. Don't get too aggressive, use light pressure, check work often so you don't go too far, and my go in the same direction (muzzle to rear).
If you are familiar with the complete disassembly you should do that prior to polishing to avoid Flitz from getting inside the gun. Clean thoroughly before reassembly.
Remember, Nickel is thin so I'd suggest doing the minimum polishing to bring back a descent finish. Also - just keep in mind that while Flitz is a very fine product, it is still an abrasive. With caution and common sense your Nickel should look good again.
Also...... just remember that while Flitz will bring back your Nickel finish to an acceptable appearance, this procedure (at least in my personal opinion) should be a one time deal and not repeated on a regular basis.