Shanghai transfer between two airports

For your case, I suggest you put forward your request for transit to your airline in advance, so that they can declare this to the Immigration Inspection prior to your visit. Then you will be granted a transit permit, with which you can get out of the airport and no visa is needed.

If you hold the connecting boarding pass, you don't need to pick up and recheck in your luggage, which will be transported to the final destination directly. Then you can just pass the immigration after landing to get out of Hongqiao and take shuttle bus line 1 to PVG to catch your plane.

Four hours seems to be a little tight, because it is a little far between the two airports. To ensure that things go well, I suggest you consult your airlines for all in advance.