The monitor specs say it has DP (Display Port), mDP (mini-Display Port) and HDMI input connectors. The computer specs indicate each of several models comes with VGA and HDMI output connectors. So my best guess is that you can connect from the computer's HDMI output to the monitor's HDMI input using a standard HDMI cable. Now, the new cable that Dell is sending you is a slightly different type that happens to include conductors for Ethernet signals for devices that use them. But maybe it also will work for you to connect between those two HDMI connectors. You do NOT need an Ethernet port for this.
Now on the the "wireless" concern. That has nothing to do with the monitor. From what I can see, your computer does not have a built-in wireless network feature, but it does have one Ethernet port you can use to connect using a cable to an Ethernet network. For example, if you have arranged to have Internet service to your computer via a cable and an router box, that box will have an Ethernet socket on it. You can connect from there to your computer's port using a standard Ethernet cable. This is WIRED networking, not wireless. So I'm not sure why you think you need a wireless something. Maybe you do not have an accessible wired network connection and are planning to access a nearby network using a wireless connection? Tell us more.