if the original has the hum then your computer recording is of course going to record that too. You now have the task of trying to "clean" that sound out. This requires some audio/video editing tools and cleaning programs. It depends on the frequency of sound that will make it difficult or easy. Sometimes you can isolate a frequency bandwidth and block it out, or try some filters. Either way this is usually a very difficult task to do. Media cleaning of video usually requires very expensive software and hardware. Sometimes you can get lucky with some simple audio filter but usually it will require looking at a wavetable and isolating the sound and trying to dampen or remove it. With just an audio file its easier to find a software solution, but with Video files, you need a program that will let you do that while keeping the video and audio in sync.
I wish I could recommend some cheap or free utility for this but I dont know of any. I do this sort of stuff on occasion but the software costs over $1000. Maybe someone here knows of some cheap solutions that may work to some degree of acceptability.