I don't think so.
Shield the electronics cavity in your guitar and make sure everything in there is well grounded. Turn off TVs, monitors, lights with rheostats (even in other rooms). Other possible noise makers; aquarium pumps fluorescent lights (the ballast units), motors in general.
A) Single coils are inferior to humbuckers? (in which case you would be wrong)
or
B) Cheap single coils will hum more than expensive single coil? (in which case you would be wrong)
Single coils and humbuckers are two entirely different creatures. No better, no worse than each other. It's all about the SOUND. You can get rid of the hum.
Try a behringer DI Box, I recently got one and it cuts the hum really well, far easier than turning down the wife.
They have a built in radar that triggers the moment you start recording, it's genetic.
Grounding has come up a few times, obviously it is huge. With that in mind, do not plug all your gear into a circuit that has ANYTHING else in it. Have a seperate, high amp breaker for the gear. Install a new, independant breaker in your electrical box exclusively for your rack.