You can qualify the procedure per ASME Section IX without recording the welding parameters because they are considered to be nonessential variables by ASME.
When you develop the WPS use the parameters you do know such as wire feed speed, travel speed, etc. If you are using a "canned" computer program, list the appropriate program number and the model number (not serial number) of the welding machine to be used.
I tend to agree with Lawrence on the issue of developing a WPS the welder can use, but we are talking about ASME Section IX. It is entirely possible to write a WPS the is of little use to the welder, but fulfills the requirements of Section IX.
ASME Section IX and reality from the welder's vantage point have little in common.
Best regards - Al