I will second the comment from Gyro regarding charging capacitors with an insulation tester and the stored energy that will be present. Now, the vast majority of modern insulation testers will contain a post test discharge circuit, however the discharge rate will vary a lot across the instruments. Some instruments like those from Sonel have quite a high resistance in the discharge circuit but will not display the reading until that voltage is discharged below the safety level, which is usually 50V. They cannot also lockout completely if the voltage is not discharged within a specified time frame.
I will add an attachment of the insulation testers I have reviewed that shows the discharge circuit resistances.
A lot will depend upon exactly what you are testing and what you want to achieve. Capacitors are very voltage sensitive and if you use too high a test voltage can be easily damaged. The vast majority of insulation testers will have fixed test voltages, common ones are 50V, 100V, 250V, 500V and 1000V. If you have a 400V capacitor, then the 1000V range will definitely damage it, the 500V range might be ok, but you are risking it a bit. The capacitor will survive the 250V range, but you will not be testing it at its working voltage. It will depend whether that aspect matters to you or not. This could be overcome with a tester that has a variable test voltage, such as the Megger 400 series, but they are usually more expensive. The only one I know of with a variable test voltage in your price range would be the Uni-T UT505A.
This raises another point in that a lot of insulation testers will have reduced resistance ranges at the lower voltages. The Kewtech KT35 is slightly different in that it appears to have 2 GOhm across the range of test voltages, a lot of instruments will only get into the GOhm on the 1000V range, and will drop to circa 550 MOhm at 500V, 255 MOhm at 250V and so on, so I would look carefully at the range specifications in the data sheets and not just the general manufacturer's brochure statements. You also suggested measuring leakage currents, not all insulation testers have this function and not all will display the actual voltage being applied either. You may therefore be looking at using a uA meter as well. The IEC standard, specifies that insulation testers should be able to drive into a 2uF load and remain stable, so if you are testing capacitors above this, it may take a while to charge them and get a stable reading.
I will add a further couple of attachments of the meters I have tested, that list their functionality and test ranges, that may be helpful to you.
Some of my blogs of the insulation testers are on here, where they are not they will be on element14, but if you want to know about a specific instrument I have tested and cannot find it, let me know and I will point you in the direction of the blog.