Please try this and let me know if that may help:
- From the Control Panel > Devices and Printers remove any instance of your printer.
- Right-click the background area and select Device Manager.
- Within the Imaging Devices section, remove any instance of your printer and keep that window open.
- Open the HP Envy 4500 software and select Connect a New Printer.
- Select the listed wireless printer and follow the installation.
- Once the installation hangs on installing network printer go back to the Device Manager.
- Within the Printers category remove any listed instant of the printer or any listed Unkwon Device, then cancel the installation.
- Select a Wireless connection again and select your printer, then check for any difference now.
- If it still hangs repeat the same steps as above, but by deleting the printer from within the WSD Print Providers section this time, once again cancel the installation and try again.
May you see any difference or will the same behavior persist?