You have two, -maybe- three options.
1: Best option: Get an external USB drive (big or small, no matter), and install Snow Leopard (10.6.X) on it, reinstall the drivers, and boot into it when you need to scan. (Or restore a backup of your last working 10.6 operating system onto the backup drive.) Don't forget to click the special options to install Rosetta, or it won't work.
2: Buy a new scanner. My recommendation: Don't buy HP. They are a sinking ship, and haven't cared about build quality, support, or software drivers, for the last decade.
3: (Unknown, advanced option.) Use an emulator, such as VMWare Fusion, to boot into the server version of Snow Leopard, and assign the USB port for the scanner to it, and hope for the best. I'd give this a 50/50 chance of working. This is not an option for novices, but maybe you have a tech genius who owes you serious favors.
A few years back, HP's board of directors was taken over by bankers, and the founder/engineers overthrown. The new board decided that they didn't have the technical competence to provide guidance in, or help make decisions regarding company investments in technology. HP then became like IBM, a 'consulting' company, and it stopped caring about quality technology or product development. They make most of their money off of ink sales, from inkjet printers. But smartphones and tablets are ravaging that market, so they are slowly dying. They make the equivalent of $17/gallon off of inkjet ink. It's an addiction that will destroy them, with the Wall Street boys simultaneously knowingly driving them into the ground, while shorting them in the long term.
It was a nice scanner. Nothing wrong with it. Just the company that made it doesn't really exist any more, other than on paper. Best of luck to you!