You might want to do a search on the whistle forum. We've discussed this there several times. Live performance is quite different from studio use in my experieence.
I will summarize my preferences as quickly as I can.
The most common setup is to use an SM58 or 57 placed above the whistle's voicing window. You'll need to stay tethered around the mic stand though. You can also choose a good cardioid condenser with the same placement.
Kind of like this.
I've used an Audio-Technica lavelier velcroed on a foam block to low whistles (not high D's) just below the window. I don't like that solution, you can pick up a lot of handling noise. But you can be mobile.
I've used an Audio-Technica headset mics (ATM-73 and ATM-75) which worked well and lets you move around too.
I've also used a micro headset which is more comfortable but the sound was not as open as the larger headworn mics.
And you should be playing a Brad Anderson whistle.
Hope that helps.
Feadoggie