How to create USB toggle switch controled by GPIO
You do not want to try running the USB signals through a mechanical switch. Too much loss of signal integrity. 

Do not attempt to switch the USB signals with a '4066 type chip. USB 2.0 runs at 480MHz when in high speed mode and the cheap mux chip will severely attenuate the signalling.

You need to manage the USB Power separate from the USB D+/D- lines. A drive operating off the USB port could be pulling up to 500 mA and that takes a circuit specifically designed for that current level to manage it's switching. 

I have built USB selection devices in the past using special circuitry on a board I designed. The USB data signals were switched via a Fairchild FSUSB30MUX part. The power to the target device was managed through a MIC2026-1YM USB power switch device. 

The picture below shows the general layout of the circuit. In this example of equipment this device had a USB Type B jack that would mate with one computer and then a USB Type A jack that would go to the shared external USB Drive or USB Stick. The other side of the USB signal MUX came from the output of a 4 port USB Hub. The input side of that USB Hub came from another USB Type B jack that would come from another computer. 



Related information in this other answer.