Almost without exception, the built-in tuners in late model rigs are for matching coax feeds up to around 3:1 and sometimes 10:1, but they are not suitable for tuning a whip or monoband antenna to some other band.
If you are thinking about this, you have a choice of one of the SGC units, or the Icom AH-4. The latter can be controlled by the Kenwood with the addition of a control circuit (see http://www.hamoperator.com/ah4/
As for the antennas, the Hamstick are cheap, but rather lossy and because they have so much distributed capacitance, not suitable for band hopping with a tuner.
I use an AH-4 and a 20 meter antenna and have written several articles about it here on eham.net. In your case, however, I think you'd be better off with one of the better quality screwdrivers especially from a cost standpoint.