I've recently had to request the recordal of the change of applicant details on a PCT application. It was a straightforward situation. I had a signed Deed of Assignment from the current applicant company to the new applicant company. The only complication was that the national phase entry deadline was less than a month away.
The first option was to submit a letter to IP Australia, which is the receiving office for this international patent application, requesting that they ask WIPO to record the change. Because I wanted to be sure that the details of the new applicant were recorded on the WIPO database (Patentscope) before national phase entry I was concerned that lodging the request through IP Australia might add to the time taken for WIPO to receive and process the request. The second option was to file directly with WIPO. It is possible to do that and that's what I ended up doing.