Find a company in your area that tests low voltage circuit breakers using primary injection. Look for a NETA company. Typical breaker test sets put out up 50,000 amps. A new or different power supply from the utility would nto be needed, since most test sets operate on 240 V or 480 V power (or equivalent.)
The actual power requirement is relatively small, as long as the voltage drop in the loop of cable or bus is reasonable, say 5 volts or less. (50 kA @ 5 V = 250 kVA).
A test set with standard CT will never make it. The impedance of the primary circuit changes by the square of the turns ratio when viewed from the CT secondary. With just 0.5 ohms of impedance in your high current circuit and a 10,000:5 CT (2000/1 ratio) the secondary impedance will be 2 meg ohms.
A 480 VAC supply could push about 0.25 milliamps into a 2 megohm impedance and get about 1/2 amp output on the high side of the 1000/5 CT.
I would be concerned about generating a "10,000 amp" field for a test. Without a gauss meter to measure the field, how do you know what field strength actually is applied to the device under test? The field strength is very dependent on the conductor configuration around the device.
For example, you could get high current by using a coax confuguration using two aluminum pipes, one inside the other, and welded or bolted together at one end. This low impedance circuit could easily carry "10,000 Amps" for 90 seconds. But the external magnetic field would be close to nil, since current in the two pipes would cancel each other. My point is make sure the test set up gives your client what they need, not what they say.