Connect to Internet using LAN NIC, but print using WIFI NIC

I have a interesting situation. We work in a large building where I lease a smaller office space. Internet is provided to all of my 4 employees but we are not connected on one "Private" network . (The building provides internet thru wired NIC). So we are unable to share devices like printers. Is it possible to create my own wifi network in our small office just to share a printer? This at the same time still haveing the hard wire connection to the internet.
This is my idea:

1. Get a wireless access point
2: The computers have 1 internal NIC "hard wired port that is plugged into wall that provides internet. The computers also have Wireless cards that I can use to connect to the new wireless access point.
3. Establish wireless connection from Wifi Printer to Wireless Access Point.
4. Hopefully all computers will be able to print.

I am not sure how to configure the NIC's so they work correctly when it comes to IP addresses and subnet mask. I know that something has to be different but I am not sure.

Thanks,

Allen

Get a router - wired and/or wireless. Connect the building internet service to the WAN port. Disconnect all computers from the building service and connect them to the router's LAN ports. Instant LAN.

JackHughs

Each of your users can use WiFi Direct for the Printer.
Virtualy every Wireless printer is capable of WiFi Direct, as are many other devices.

You can do it the way you suggest but it is more complicated.