On his site, Mack Hoover recommends a non-toxic brass polish called “Never-Dull”, available from The George Basch Co., Inc., Freeport, New York 11520.
I am intrigued by those mini-steam things (for metal whistles). No abrasion, no chemicals..hmm…I guess the only issue would be glued joints on delrin…
Yep, the jet on the steamer did a great job through the windways, though I did run the pipecleaner through them too. Of course, Aulos recorders are famously tough. I’m not sure the plastic heads of the mass production whistles are as hard and heat resistant. I’d be a bit worried about the edge of the labium. Wouldn’t want to warp it! Would be fine on delrin or (no glued parts) all-metal whistles though; but you’d need to be cautious about their heat conductivity! Thick rubber gloves probably advisable.
BTW, I’ve just been reading up (for other reasons) on Renaissance Wax (recently mentioned over on the Flute Forum) and it sounds as though it would be an ideal finish for whistles in all materials, but especially if you want to keep your metal ones shiny! Of course, if you prefer a dull patina of age and use/abuse, corrosion products and gunge… 
These guys’ (museum conservation product specialists) other products could be of use to some of us too, perchance? I think some of our serious makers might find the Renaissance Wax worth checking out as a regular production finish? Check it out on this link.