Increased capacitance is not a good thing for your GZ34 rectifier tube so moderation should be exercized. If the grounding is not optimal, and it's usually not when a multi-unit can cap is used, you can get a buzzing type hum that's hard to get rid of. How many ground wires go to this cap board? Did you replace the 1000uF caps and the voltage doubler that powers the preamp tubes heaters?
Regular instrument cable should be fine. Some types of coax intended for radio frequencies can be micophonic but any "audio" coax should be ok. Look on the schematic and there is a 10 ohms resistor between the power amp's ground and the ground to the preamp. Check it with an ohm meter to make sure it's still good. There will probably be a short across it when the preamp is plugged in (that's ok).
There is one little problem that may come up. The GZ34 is supposed to delay turn-on for 10 seconds or so. This prevents the 500V B+ from getting to the 450V cap in the preamp. When the amp was made, the caps could stand over voltage for a few seconds but todays caps arent quite as tolerant. If you replace the GZ34 with solid state diodes, it will be something to be dealt with.