Classic/Antique Car Repair: Steering wheel wobble at high speeds

Question
I have a 39 Ford with a stock suspension,except for modern type shocks front and rear.  I am looking for some advice that would cause my front end to shake. I had the tires balanced years ago and had a front end alignment years  go also. As the tires are old would flat spot cause the vibration at high speeds only or would the steering wheel shake at a lower speed also?

I also grabbed  the front tire from the top and pulled it toward me ( while car was on the ground ) and I can feel slight movement from both front tires, I have not checked the wheel bearings ,but my thinking is that the wheel bearing need to be tightened only. I do not believe the Bearing are bad. Would having a very slight wobble ( when I pull on the top of the  front tires ) cause the steering wheel to shake at high speed?  Having the front end aligned and the front wheels balanced along with the rear wheel balanced years ago cause the shake. I do not put a lot of mileage on the car and do not drive erratically since I had those procedure done years ago. Possible they never aligned it correctly or balanced the tires correctly years ago?

Answer
Ok, it's not a Model A, but here are my thoughts.  Get the alignment checked and have the wheels checked for balance.  Since it has been a long time, I would spend the money.  They might not charge you too much for just a check.  Lack of toe-in can cause the prob.  Tighten the brg's, but not too much.  Ice in the tires can cause this, but I doubt if you have that.  It's easy to put a tire on with water in it.  Just a thought.  That was a prob we had in the plants.  Check your strg box.  It may need to be adjusted.  Take the pitman arm and yank on it and look for any loosness , in any direction.  It should be super tight.   You better check all of the tie rod and drag link ends.  Stick with it until it runs smooth.  It should.  Bald tires can also screw things up.  Good luck.  jack