Steering shake under braking or otherwise is a real PITA.
Youve checked the ball joints.
Other things to check on the front:
Tie rod ends, inner and outer. Wheel bearings. Uneven rotor
wear. Hub runout, and of course wheel alignment.
If aftermarket wheels are fitted, hub rings are needed to center the wheel on the hub spigot as well as for safety. Plastic ones distort with the brake heat so metal ones are best. (Sometimes, without them you'll never get rid of wheel shake).
A clock gauge with magnetic base is a good investment to check hub runout, as well as rotor runout. I found that even brand new rotors can still have runout, but this can often be fixed or reduced by indexing. (swapping their position on the wheel studs). You can even index the wheels this way too if you are that keen.
Just one more thing with alloy wheels; always tighten the wheel studs using a torque wrench with a 'star' tightening sequence. I use about 80 ft/lb
Good luck with it.