Do you have, or are you aware of the tyres having been treated with anti puncture fluid?
As experf stated, if you have any form of fluid in your tyres it can settle overnight causing a slight shimmy when you first drive the car in the morning.
I seem ro recall reading about this anti puncture treatment and you are supposed to use a measured amount per wheel, if too much is used it can lead to an imbalance of the road wheels.