For ASME VIII Div. 1 designed but non-stamped vessels that fall under PED 2014/68/EU, welding procedures do not need to be qualified to ASME Section IX.
According to PED requirements, the Procedure Qualification Record (PQR) must be qualified according to ISO 15614-1, and the qualification must be approved by a Notified Body.
The Welding Procedure Specification (WPS) can be based on the design code (e.g., ASME VIII Div.1), but the PQR qualification must follow ISO 15614-1 for CE marking.
In summary: For PED compliance, use ISO-qualified procedures approved by a Notified Body; ASME IX is optional if the vessel is not ASME-stamped.