A big cause of a high-speed shimmy-shammah is a mis-balanced wheel. You could also have an ovulated wheel from having the spokes tightened too much in a particular direction.
Another could be your headset bearing not being up to scratch with a lot of play. This also causes it quite often. Also, a bent frame will almost always make it impossible.
Also check your calipers are centred, as this rubbing on the wheel can cause unusual behaviours. Another thing to check is that the quick-releases are tight and that the wheels (front and back) are perfectly centred inside the frame dropouts. Check also that the fork itself has no kinks and hasn't got any play.
Also, make sure your body position on the bike (saddle height, angle, fore-aft adjustment and your handlebars) is optimal for you, as this will help your balance greatly. And, check the frame size is suitable for you. For example, I ride a frame-size smaller than I'm recommended to so that I have a high seatpost, and I can run slightly shorter cranks for faster speed, yet lower acceleration. (However, I can still achieve dank wheelies! :3 )
Forks are designed with a slight spring to them to absorb road vibrations, just like a leaf spring on old cars and vans. If a fork is made too stiff, it can be a challenge to do no-hands on a frame.
Honestly, it should merely take a bit of practice to do no-hands again on this bike, as I found out from going on a road bike to a criterium bike.