If modifying the Skylon isn't acceptable...

Then just carry up the nuclear thermal engine as cargo.  A 4000 MW nuclear thermal rocket could fit inside the Skylon's cargo bay.  Perhaps you don''t need that much thrust.  A smaller engine, like a 800 MW engine could be fired longer to do the job.  The advantage of a smaller engine would be that it would be easier to shield.

That thought gave me an idea.

What if you were to use the Skylon to go to Mars and back?  The idea is to use the nuclear thermal reactor (NTR) as the propulsion device to and from Mars.  You'd fit it inside the cargo bay, and hook it up the the hydrogen tanks.  Put a couple hard points at each end of the Skylon so that it can be spun up for artificial gravity for the long trip to Mars.  On one end, there'd be a habitat.  On the other end, there'd be a lander.

At 3 RPM, you'd get the same artificial gravity Von Braun was talking about with his space station concept.  The length of the Skylon is comparable to the diameter of his space station.

You would need several launches to get everything in place for the trip.  You'd need to refuel the hydrogen tanks.  You would need to deliver the habitat and the lander.

One advantage to using a Skylon this way would be to have a ready made way back to the ground.  The same vehicle that gets to orbit can return from Mars.  As mentioned, there wouldn't be a need for separate hydrogen tanks for the NTR.  That would reduce the number of assembly missions.

Perhaps only three assembly missions would be needed.  One to deliver the Skylon and NTR itself.  Two, to deliver the habitat and supplies.  And three, to deliver the lander and fuel.  Note:  the Skylon doesn't have to do all the lifting.  A heavy lifter could do the rest.  Just dock all of the pieces together and you're ready to go.

Perhaps a fourth mission could put into place a methane/lox generator on the Mars surface.  The lander could be used multiple times in order to refuel the Skylon's tanks for the return trip to Earth.  You would want a water source, though.  Mars has plenty of water.  Another possibility would be to carry all return hydrogen on the initial assembly.