Rad Alt would not normally be required for a Cat 1 aircraft, although I would expect one to be fitted for EGPWS/TAWS (an essential safety aid). Or does (your) TAWS use geometric altitude?
The equipment requirements for All Weather Operations (Cat 2-3) are in
CS-AWO.. For the US, AC 29 is similar, but not identical.
Operational (national) approvals might vary these requirements, but recent European tightening of the rules should align GA all weather ops with commercial ops; however the US might differ significantly with their FAR 121 / 135 operations.
Also the new generation of technology may be challenging some to the existing rules.
Crosscheck with EU OPS 1, but that might only add to the confusion !