When Morgan converted to bearings they increased the castor angle to make sure shimmy did not occur. Some owners of previous models experience some shimmy after fitting the bearing kit, but not all. It seems to depend on many small factors. My feeling is that you should remove the blades and try it. If you experience shimmy it can be resolved with a low cost steering damper.
There is a thread on steering dampers
Here PLEASE TAKE NOTE:-
Further update on the Steering damper, it is now removed, having taken Rosie to New Elms to get her checked over and steering checked out Darren noticed the bracket to the steering damper that clamps around the track rod end was precariously close when steering and at some point had in fact rubbed against the end of the rack. This could de EXTREMELY dangerous and lock the steering. Darren removed the rack to adjust the spring tension on the column end, and when he refitted it, re-aligned it so that the track rods are now parallel to each other and are now even closer to the rack so fitting of the damper is no longer possible. However it is no longer needed as I now have no wobble at all. Darren said that he believes any Morgan if correctly set up should not get the wobble. correct track rod and steering rack alignment are the key I believe.
So to summarise if you are going to fit a steering damper be very certain to check it clears everything with ample space when the car is sitting on the ground, at all steering angles. You need to bear in mind that hard braking or severe suspension travel can move the clamp around the track rod very close the the rack at a specific point of turn. (this is also on the other thread)