Shimmy Shake

First check behind each wheel to see if there's debris stuck on one. This is a lot more common with cast wheels. Chunks can break off due to corrosion and stick to the brake rotor, then if that wheel is reinstalled in a different orientation, that debris prevents the wheel from sitting squarely against the rotor. In this case it would be more likely a chunk broke off your old wheel and stuck to the rotor, but chances are the problem would still be there when you put the old wheels back on.

My suspicion is you simply have a bent wheel or a tire with a broken belt. For a broken belt, you'll see the steering wheel oscillate back and forth a little with each tire rotation as you drive slowly, as in a parking lot. Broken belts can also be found at a tire and alignment shop. Besides the common tumor or raised spot that is easy to see, there can be less-obvious things that it takes a specialist to point out.

There are other things that can cause a steering wheel shimmy, but you already ruled them out by observing it was gone with the old wheels.

You probably need hub shims to "center" the wheel on the hub. Such as these:

They are sold in different thicknesses, so you need to measure the hub & wheel and then subtract one from the other to give you the thickness you need.

Thomas