Predictive windshear is a function of radar, not EGPWS.
You're right that you need radar for it to work. I'm not sure as to whether it lives in the same box as the EGPWS: these things tend to get lumped together in manuals for brevity...
Reactive windshear is an EGPWS function.
I think you might find that this feature existed in some GPWS units before EGPWS came on the scene, as you don't need position data (which many of the EGPWS features require) for reactive WS protection.