at this voltage, we generally only perform an insulation resistance measurement between the metallic screen of the cable to earth. This should give you a reasonable indication as to the condition of the sheath. It is only when going to the higher system voltages that we will perform hv tests on the outer sheath.
if you are performing hv tests, you should be performing insulation resistance measurements before and after the test, to determine if you have caused any damage from the test voltage being applied.
10 kV seems excessive for test voltage on sheaths on that voltage cable. The IEC 60299 reference is good, but you need to ensure from the manufacturer that the oversheath was manufactured to this standard. If not, then you need to ask the manufacturer what tests you can do, and what (if any) test voltage to use. You can't just take the after laying tests from this standard without the manufacturer designing the sheaths to the standard, and performing the type and routine tests in the factory (which is considerably higher than what should happen in the field after laying).
on the test set size, personally, I like a test set that will produce a decent amount of damage at the point of fault (assuming it is testsed at the correct test voltage as above) because the smaller the test set fault current, the harder the fault is to find once you have one.
ausphil