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Yes, it is possible to hook the printer to one computer with USB and also use wireless on another computer same time. Do you know your WiFi name and password ?
Yes, it is possible to hook the printer to one computer with USB and also use wireless on another computer same time. Your laptop should already have an wireless/WiFi chip/card, so you don't need to buy new dongle. It works with laptop's WiFi. But first you need to connect your printer to the WiFi network.
There are two ways to connect the printer to your WiFi network. One is by connecting to the WiFi on the printer itself and the other is by using your computer to setup Wireless on your printer.
Method 1 (on Printer itself):
Method 2 (using your computer):
On your Laptop (for this, use laptop, connect the printer to your laptop with USB cable temporarily), then go to this website --> http://support.hp.com/us-en/drivers/selfservice/HP-Photosmart-6510-e-All-in-One-Printer-series---B2/5058334/model/5191793
Then download the printer software. Open the printer software and follow the onscreen instructions to install it. At the end of installation it will ask you to setup Wireless connection. Select it and continue on screen instructions to setup WiFi on printer. Once you did that, you can disconnect the USB cable and connect the printer to your PC. Then you can print from your laptop via WiFi.
If you have any difficulty on following the steps above, please let me know and I will continue to help you.