Is that the only firearms you have? If not take them all with you. If you can borrow some that way you have as many as you can on your CCW. Taking the wheel gun is a big plus though. That lets you carry anything from a 22lr to the Taurus Judge that shoots 410 shotgun shells.
I don't know how much or even if they charge you to add guns to your CCW. But down here in Clark county it's $25 each time you want to update your card.