If you leave the U-lock at the parking rack, you may want to carry a short cable lock for shopping stops. 2 locks are always better than one; if they can crack the U lock, your long cable is useless. I dont find it a problem to carry the U lock. There is a thread on ways to carry U-locks and my suggestion (top of the rear luggage rack is there)
Beware of using any QR skewers on a bike that you leave unattended. Some people mess with them, others remove them altogether even if the wheel is locked.