If you can't find shims, try using Copaslip on the backs of the pads. That can help. Or maybe make your own with some tin snips. A drinks can is probably flexible enough and easily cuttable.
https://www.google.com/search?q=copaslip
Also check that it's not your brake shields vibrating - in our wetter/saltier climate they corrode and start to break up. I've also had small stones/gravel stuck between the shield and the disc which makes a hell of a noise - interestingly not all the time, only with the steering in certain positions and under braking.