Good question to pass on to Errata, I'm not sure Whip/Monofilament Whip falls under Exotic Weapons. It's grouped with the "Other" melee weapons in the gear chapter, and the heading text implies it's part of the Close Combat skill. I'll pass it on to Errata to see if we can get an official word on that.
As for the Exotic Weapons skill, it sounds like it is all ranged from the Combat section that lists off blow-guns, lasers, assault cannons*, and grenade/missile launchers as the Exotics. I believe it should be the "generic" type of the weapon as the specialization, since the archetype for the Weapon Specialist has Exotic Weapons (launchers)
*Which raises another point about Assault Cannons, since the Panther is listed under Machine Guns and not Exotics in Gear; passing this on to Errata as well.