Polishing silver bullet

So my silver bullet nozzle pretty dull (throwing it in the dish washer might not have been the best plan lol), it's an expensive piece that many of us probably have so thought I would ask here for advice about polishing up that aluminum beauty.

Some fine steel wolf or 400-600 grit sandpaper, make your own polishing compound with vinegar and water. Add in some elbow grease and you’ll have a shiny new bullet! Don’t use a chemical polishing compound, treat your bullet like a kitchen utensil!

https://www.redlabelabrasives.com/blogs/news/how-to-polish-aluminum-the-full-guide?srsltid=AfmBOooEsYk-DV8o251XgtWdnoVUU8yv8PhrJdobZpOE1AfsXeuGmYv4

You will scratch it with 600 sandpaper, believe it or not, that's too course. Get some semichrome polish and use a soft cloth. The hoseman

Has it also gotten somewhat grey in color in addition to being dull?

Cameo makes various powdered cleaners for metal kitchenware. Their stainless steel and aluminum cleaner is excellent. It does not scratch at all.

Grocery and discount stores in the US carry it routinely, near dishwashing liquid detergent and dishwater detergent. You're looking for this: https://www.walmart.com/ip/Brillo-Cameo-Aluminum-Stainless-Steel-Cleaner-10-Ounce/119089650?classType=VARIANT&from=/search

Try Never-Dull ...... I use it on my aluminum wheels. Best stuff I've found.

Amazon or Ace Hardware.

Might try toothpaste with a very soft cloth.

Dishwasher detergent reacts with aluminum, that is why they say never put aluminum pots in the dishwasher.

Just use soap and water and boil if needed.