For removing rust from finished parts, it's best to use a chemical rust remover.
WD40 has a Rust Penetrator formula that works well on surface rust.
I've also used something called Evapo-Rust. I buy it at Napa Auto stores. Best to call around and ask if it's in stock, as stores seem to sell out often. I use it on rusted tools, power tools with steel parts (drill press, bench vise, bench grinder, etc.).
One warning on the Evapo-Rust -- if you leave it applied/soaking too long, it starts to turn the metal a dark color. Basically, you trade the oxidation for some other chemical reaction that now has to be cleaned off. A wire brush attachment on a cordless drill works pretty well, but adds work. Best to just monitor the progress and clean the stuff off once the rust is gone. The dark stuff might be caused by the rust mixing with the product -- not too sure. For larger parts, I soak a couple of paper towels in the stuff, place it over the rust, and leave it for a few hours. Then I check back every hour. Leaving it overnight is often too long.
Evapo-Rust is a great rust remover, but I'd try it on a spot first, to make sure it's not going to damage the finish, too.
Even after removing the rust chemically, you still want to touch up the spot/s to hide the damage and protect it from rusting again. They sell firearm finishing and touch-up kits in different colors. I've looked online, but the places I found won't ship to Hawaii. I think someone said Young Guns had it once, but never got around to checking.
The WD40 stuff works well, but not as thoroughly as Evapo-Rust. I'm in the process of cleaning some surface rust off a firearm now with it. So far, it's doing the job, but taking a couple of days applying with cleaning in between. No damage to the finish that I can see.
I'd never take anything more abrasive than a toothbrush to a finished firearm surface.
All things being even, I'd say this is a good reason to use something like FrogLube on all your guns. You can't always control the environment where your gun will be, nor dictate how long it might be in a damp case. If water gets on it, you need something besides Ballistol to protect it.
There are threads on here and videos and articles comparing firearm rust protection products. Once you have the finish repaired, you still have to worry about all the pieces and parts that aren't as well finished.
Hawaii = Rust = Sucks.