If I recall correctly there are some TAWS alerts that can trigger on approach, e.g. high sink rate or too much bank angle below a certain height. These may depend on a Radalt input to ensure they are accurate and, perhaps more importantly, don't get triggered falsely. Baro/Inertial/GPS height may not be good enough by itself, particularly when descending in the landing configuration (as you probably know, on some aircraft types with high throttle settings + full flap/slat and gear down are not usually as amenable to static pressure error correction as they are in the cruise configuration). The addition of Radalt data in to the mix improves the accuracy in the height solution for the final phase of flight.
Having said that, given that TAWS almost certainly uses some form of Kalman filtering to fuse the data from the different height sources, I would suspect loss of the Radalt would not be a major problem. It would just reduce the accuracy slightly when operating close to the ground, particularly on approach, so the system should respond by increasing the alert thresholds a bit. It might increase the false alarm rate slightly but I doubt it would be unsafe in any way. Therefore I suspect one Radalt would be sufficient.
As to specific regulations and requirements, I would have a good look through the EUROCAE and RTCA websites and FAA ACs to see if they have a specific MASPS document or similar (if you haven't already!).