If you stick to 69.9mph you’ll never experience the shakes and you’ll not get any points on your licence…
(unless you’re doing that speed down the High St too)
First thing I’d check is whether the wheel bolts are done up tight.
Other than that there’s the fact most roads look like the surface of the moon at the moment so it’s quite possibly a dinked rim, or a wheel weight could have come off which is feasible too.
Even a defective tyre is not out of the realms of possibility.
Check the bolts, drive to a reputable tyre fitter and get the wheels and tyres checked paying special attention to the inner rims.
Also when doing the alignment it’s not impossible that if they adjusted something it might not be correct or a bolt might not have been properly tightened. So that’ll be step three, going back there if all else checks out ok.