If you got a ppd file of hpcups 3.9.12 you should be able to print from your laptop without the hardy drivers. In most cases the ppd files are placed in /usr/share/cups/model/
If you haven't got this ppd file, just take a look at the link below. There are also more recent versions of the drivers.
Download the driver you wish to install (for example the tar.gz file) and open it with your favourite archive manager. extract the ppd file judging on the model names shown in the ppd directory. In this directory there are also tar.gz files. When opening these the ppd file itself is there. Copying it to the /usr/share/cups/model directory will give you the next option:
Add a new printer at localhost:631 and in stead of selecting the model, click 'providing ppd file:' and browse the file in /usr/share/cups/model. Now the new driver will be applied. If it works, you may delete the other less functional printer of course.