Hi dnf999
There shouldnt be a problem using an external usb drive, regardless of the number of partitions on it.
The quickest and easiest way though would be to just add the 20 gig drive as a slave drive to the new pcs drive, just set the jumpers as slave and connect to the IDE cable and the power leads, its not even necessary to physically attach the drive to the case if its only to be a temporary measure.
Then copy everything across from the old drive to the new one