I am not from Laminar Research; just another flight simmer.
A USB stick is just another form of "external drive".
Provided you are not using the 3rd party hybrid called steam on your old computer X-Plane should be installed as C:\ x-plane or C:\user name\X-Plane or on some other dedicated directory of your choice. When you find it move your mouse cursor to that directory and right click on the directory. Then from the displayed window move your cursor down and right click on properties. The window that now appears will tell you how big the directory is.
To then copy X-Plane to a USB drive, the USB drive needs to have a capacity in excess of the size of the X-Plane directory.
The largest size USB drive I can purchase down under is 128 GB. If your directory is larger then you will most like have to copy as "Bits and Pieces" as RUSS has indicated above.