The outer vinyl or plastic on the steering wheel is wearing off exposing the foam underneath and just feels weird driving. I've never had a steering wheel do that before but I'm out of warranty and want to take care of it. The XLT wheel on my truck only has the buttons on the left for cruise control.
The part number is 2011-2013 FORD F-150 #BL3Z-3600-BC

Can I swap it with part number (I don't know) my mirror adjust is on the door and the only other wheels I've seen have the mirror controls on the left side of the wheel.

 

Why swapping the steering wheel. You can always get a nice steering wheel cover. From my experience they last longer. And if you still wanna swap then you probably wanna look into the wooden style they look like they last forever
Good luck, Moe

 

get a wheel from an online junk yard in leather or as previously mentioned get a quality leather wrap and take your time applying

 

Wheelskins make a great leather cover. I have used them on 4 different trucks. Check out ebay as they usually have the best prices. I bet a new oem steering wheel will cost at least $500. Then you have the hassle of switching it or paying someone to make the switch. A salvage yard could save you some $, just got to make sure what condition the part is in. Good Luck!

 

Like JeffroMc above I've done the wheelskin for my last several vehicles. Makes it feel like new and thicker to boot, about $50 delivered.

 

I have changed out a few steering wheels, upgraded previous truck to raptor wheel even. It's super easy and I completely dispise steering wheel covers, they always have a weird smell that rubs off on my hands and makes the wheel abnormally thick. Just my opinion though. I can pm ya pics of the steps to change out, the main thing will be swapping with a similar control/harness...which in the case of what you posted pics of will be there, but the synch and radio controls on the right won't be active on yours as it won't support it. Best bet is to find another similar wheel on ebay, or local craigslist they are out there.

just fyi...i bought my raptor steering wheel for $150 from ebay, stx versions were cheaper. I had synch on mine so it was a 1:1 matchup.

 

They want too much for this one, but it's what you need.
http://bit.ly/1lID99v