"I donot wish to use the keil dongle with two computers at the same time."

OK

I have seen a dongle (though not the Keil dongle) shared between 2 computers on a simple printer 'T' switch.
But this was over a distance of ~20 feet - not metres!

"I need the information on how to send the printer port signal over 20 meters."

That's way beyond what the printer port's designed for!
Knowing how awkward the Keil dongle is (it messes up the Triscend JTAG access), I doubt that it would work properly via any sort of active extended device.
In fact, I don't believe that it works properly at all!

But if these PCs are 20m apart, and you're assuring us that it's not 2 people using them simulataneously, you surely can't be swapping between them that frequently!?
Why not just take the dongle with you when you hike off to the other end of the lab?
You could buy a couple of short printer cables to make the dongle connection easily accessible?