Is it possible to take a cable from one USB device and attach it to another?

So my mouse's connector broke, and I have this old USB keyboard lying in my desk so I'm wondering if I take them apart, if it's possible to take the cable from the keyboard and jerry-rig it to the mouse? If it is, would I need any specific tools (Soldering iron, hot glue gun, the like)?

the connections are likely the same, but there's more than a single copper wire inside of a USB cable. You will need to cut both sides, strip the wire and solder on 4 (I believe red, white, green, black) wires to each other, electrical tape them individually then you can likely wrap the full set together.

Theoretically, it is certainly possible as the pin assignments are universal with the USB standard. The problem wlll be in separating the wires from each other in those molded connectors and cables. Yes, you would need a fine-tipped soldering iron and resin core flux (as opposed to acid core that will corrode wires and components). Resin core flux is what is used for soldering electronic connections. Acid core is used for soldering sheetmetal seams.