I agree PWHT would be a logical step but like I said I don't know your application and that maybe the determining factor.
The HAZ will be very hard no doubt but the "as welded properties" maybe more desirable to the designer.
A procedure can be qualified with out PWHT. That is one of the primary reasons for using 309L and Inco filler material to avoid the need for PWHT. I am not suggesting you use either just replying to your query.