You don't need to unplug anything if you can log into the switch and know the computer names. You should be able to get the MAC address of each computer. How you do this depends on several things, but there are multiple ways to get it without having to be physically at each computer. One such way is to look at the DHCP Server for the leases. Once you have the MAC address then you can look at the forwarding or MAC table on the switch. Each MAC address should correspond to a unique switch port (note that it can also be seen on other switches uplink ports). Using this method you can gather that part of the information from the comfort of your desk.
Since you know the physical location of each PC, now you just need to trace from the switch port to the patch panel port and label that patch panel port with the cubicle number. If there are multiple ports in each cubicle (and there probably are), then you do need to see if they standardized how things are plugged in at each cubicle (i.e. we always put the workstation in port 1, VOIP phone in port 4, printer in port 3, etc.). You'll want to make sure that you label the patch panel ports accordingly. For example, if a PC is in port 1 of cubicle 1, then I might label that port on the patch panel as CUB1-1, or something along those lines.
For the times when that method doesn't work, you should really invest in a good toner set. We use the Klein Scout Pro 2
for generating the tone, and just about any tone receiver will work for finding the signal. The Scout Pro 2 also has the ability to put identifiers in your source ports (the cubicles) and you can move from port to port on the patch panel to identify each one. The identifiers are faster when you know which patch panel you're going to. If there are multiple ports at each cubicle, you could start with identifying the unused ones. You'll likely notice a pattern and be able to identify the other ones without disconnecting anything (if the MAC address method I mentioned above doesn't work).