Do you have a rake kit?
If not, my experience riding trikes without rake kits is very limited but, I remember testing a Yamaha Venture Trike. There was a slight wobble that smoothed out above 35mph. Installer told me that was the "nature of the beast". I quickly moved on!
If you have shaking handle bars up to and beyond 70, first thing to do is NOT ride until you or if you can't, someone that knows how, checks the steering head bearings and then the torque on them.
Lift the front wheel off the ground and check for movement for/aft, side to side of the forks.
That's the simple answer and the easiest fix.
That wobble can be caused by several things. The most difficult one to correct may be misalignment of the rear end!
If you find the fork bearings to be OK, I would suggest you locate a trike conversion installer and have that person check your trike for you,
Let us know what you find please!