No tray. I'd break it. And I'd hate it ever before.
I tend to place the keyboard on my desk, rotated slightly to the left, then my left wrist rests on my knee, as I sit with my legs crossed most of the time (and also turned somewhat to the left.
And my touch-typing technique is non-standard. I have more keys under my left hand than normal and I hit some keys with either hand depending on what's the fastest or most natural at a given moment,