Keep in mind chrome is porous. It is not a protective, not even rust resistant coating/plating. It's the nickel (over copper) that is non porous protective. Early cars had nickel plating as a protective decorative finish. Chrome plating was added to make parts shineyer. Then they started chinsing on the nickel because it still looked great for a while, until the rust started!
IMO cosmolene is over rated. Weapons and vehicles needed to be repaired in the field with parts litterally drop shipped an sitting who knows where until used. Cosmoline and special oil impregnated kraft paper were used to hopefully protect parts for maybe a few years. They didn't have zip loc poly bags back then LOL!
In the 80's I was doing a mechanical resto on my near mint one owner 37 Ford Deluxe Coupe. I spent months sometimes years searching for NOS parts. This was before the net so a lot of snail mail and long distance calls (many like $5/min.). Ford engines and other mechanical parts were used in various military vehicles. Many of these parts were same as used on 37 Ford drive train. Like Paul Harvey used to say "here is the rest of the story". WWII military surplus parts were about 40 years old. Supposidly great source for old Ford mechanical parts. $100s of dollers of NOS Ford parts started arriving at my door. A package would come...it's like Christmas...Oh Boy this one is the NOS cam I ordered. Get out the big pan, kerosene, rags etc. two hours later in my hand is a nice deeply pited rusted absolutely useless NOS cam! Engine bearings, same story, piston rings so rusty some were falling apart. This useless trash was in fact NOS!
Cosmolene or any other protective coating like say epoxy paint tends to concentrate the corrosion damage where the protection is violated. Zinc plating "galvanizing" actually protects the part galvanically even in the area were the zinc coating is damaged.
Back to the point. If the so called chrome plating has a good copper/nickel plating before the chrome it will probably be fine without cosmolene, grease or a big zip loc bag!