Which 2-seat 4th generation fighter/engine/configuration (de-militarized) would the best supersonic long-range civilian private transport?
"Best" is subjective. At the very least, you need to prioritize your criteria for the question to be fully answerable.

I'll give a short answer based on your current criteria:


Civilians can potentially buy any fighter jet, provided it's demilitarized, depending on their relationship with the government. The US certainly won't sell an F-22 or F-35 to just any individual or country, but George W. Bush might have a shot. Absolute monarchs, of which there are quite a few left, might buy a jet for their military and appropriate it to themselves.
No recent fighter jet is even remotely close to being flyable by someone with only a PPL, even with every endorsement out there. The ground is severely obstructed in these planes while landing, their stall speed is uncomfortably high, their control sensitivity out of the ballpark. The only civilian-piloted case for them would be a retired fighter pilot.
No fighter jet is capable of long-range supersonic flight. The supersonic range of all fighters is extremely short - a few hundred miles for the best-case. The only military aircraft capable of sustained supersonic flight are the B-1 and the Tu-160.
Not much weight can be removed from a fighter jet before it's easier to buy two fighter engines and build an experimental aircraft around them instead. The gun and the main radar is about it.
If one had to choose specifically a fighter jet, the best choice is perhaps the Su-34, thanks to its amenities, as well as its long range and large useful load.
Of course, with unlimited choice, the Concorde would still be the best. Out of military aircraft, the Tu-160 - it's got enough in common with a supersonic airliner to convert, and it's the largest.  
If SST and bombers are out of the picture, you'll get where you're going fastest in a fast bizjet like the Global 8000. The F-18 is not suited for the job at all, as it's not even able to supercruise. A fighter jet can be fun to fly (if you can do that) for the performance, not for its usefulness as a transport.