IF the shotgun in question was a Merkel, Purdy, Holland & Holland- YES- it WOULD be a big deal. But those are collector guns worth more than my HOUSE!
For light surface rust, wet down good with a decent gun oil (Remoil works) let soak, and rub with a soft, clean cotton cloth. You can get more aggressive with 0000 steel or brass wool, and light oil. A really stubborn spot of rust- find an older COPPER penny (new ones are copper plated zinc) and use the edge of the penny to scrub LIGHTLY. Follow up with oil/cloth.
For times you need a penetrating oil, 50/50 mix of acetone and ATF (automatic transmission fluid) apply, let set, buff with cloth. Careful- is flammable.
There is also a polish called FLITZ that can be used on light rust without screwing up the blue. But remember bluing is a thin layer of black iron oxide- anything used too enthusiastically will buff away that thin layer.