Pistols are not part of the equation here. The options are bushwhacking in dense northern scrub with a full-length rifle/shotgun, carrying bear spray / bear bangers, or taking nothing at all.
Is that due to legal issues? Are handguns verboten there? There are several wheelguns with power that rival rifles and shotguns. A .500 S&W or .454 Casull will flatten even pretty big bears.