Using a trigger coil, it won't arc if you don't exceed its design flash voltage, they are not supposed to arc at the design voltage and require a trigger coil voltage to get it to flash. i would not trust that 20 KV bridge to be good, if one of those diodes are bad, you will pay a lot more to replace it than the whole thing costs. If you want to risk it, at that price, not too bad, but be aware if you use a full wave bridge with only capacitive filtering, the unloaded peak voltage the capacitor charges to will be about 1.6 times the RMS AC voltage being fed into it, under load about 1.4 times which is moot for this application, as you will charge the caps to peak. If you want 1000 VDC, the AC into these diodes will need to be 625 volts for a top voltage of 1000 VDC when the capacitor is fully charged. A bleeder resistor across the capacitor, depending upon the resistance, will dampen the peak charged voltage a bit, but i would put one across it to save you from getting zapped later, if charged the day before and getting across it somehow. Using a variac you can adjust to the dc voltage you want but be careful, if using an electrolytic capacitor, i wouldn't charge it to its top voltage rating, keep it 25 percent below that. i had one blow up on me a few days ago, as they age, or if used old surplus stuff, the more likely for a failure if running at their rated voltage, accidentally exceed that voltage too far and they get hot and build up pressure until they blow. Although some electrolytic capacitors have over-pressure vents, if the pressure builds up too fast, they won't stop an explosion.
i built a 2kv high voltage power supply some years ago and put a safety bleeder resistors across the capacitor, just as a double check before working on it, after turning it off a few minutes, i measured the voltage across the capacitor and it was fully charged! a brand new out of the box wire wound bleeder resistor i had just received from Mouser electronics had an open! there was no resistance due to that failure, that could have killed me if I had assumed the resistor was good.