Can a Bard/Barbarian use Performances while raging in combat?

Yes, you read that right. I’ll also mention that when the character is made, it’ll be 7th level, so the levels of Bard and Barbarian will be split. She likes the idea of raging to greatly increase her effectiveness in combat, but also likes the performance system in Pathfinder, so I’m trying to make it work. Now, I know that raging as a barbarian makes Charisma, Dexterity, and Intelligence based skills unusable (except Acrobatics, Fly, Intimidate, and Ride), so that rules out Performance checks because they are Charisma based. I was looking through the wording though and it looks like some of the Bardic Performances and some of them don’t seem to require a check. For example: Inspire Courage reads…

A 1st level bard can use his performance to inspire courage in his allies (including himself), bolstering them against fear and improving their combat abilities. To be affected, an ally must be able to perceive the bard’s performance. An affected ally receives a +1 morale bonus on saving throws against charm and fear effects and a +1 competence bonus on attack and weapon damage rolls. At 5th level, and every six bard levels thereafter, this bonus increases by +1, to a maximum of +4 at 17th level. Inspire courage is a mind-affecting ability. inspire courage can use audible or visual components. The bard must choose which component to use when starting his performance.

Nowhere in that text is a Perform check required and the only condition to continue a Bardic Performance is a free action, so this should be possible right? A few performances do either require the Perform check (Countersong for example), and others conflict with the concept of Rage (Fascinate requires no Perform check, but also doesn’t work in combat, which a Barbarian should DEFINITELY be doing if they are raging). I’m fairly new myself, so I’m not quite sure of a lot of nuances to this, like whether you can make Perform checks while brandishing a Greatsword, if this particular class combination would work, and if it did, what combination of levels should be used. Any help would be greatly appreciated.