Hi.
First the source of the hum has to be determined.
Starting with the assumptions that the Champ in question:
#1 Is grounded properly.
#2 Has its original guts, IOW hasn't been modified.
#3 Has the original AC filament supply, without hum balance pot.
#4 Has the original PS caps.
#5 Has the tube rectifier.
#1 If the grounding is faulty You'll get hum, a bit or lots depending of the situation.
#2 Any unprofessional modding tends to leave the wires inside the chassis untwisted and in a mess. Tube amps generally require a neat, well thought wiring harnesses to be reasonably quiet.
#3 Modding AC to DC usually reduces hum, but might change the sound. You can also put a hum balance pot there.
#4 By now the caps are most likely at the end of their journey, replacing all the electrolytics will reduce hum, will also change the sound but usually NOT in a bad way

.
#5 Being tubes, tube rectifiers will induce some hum and as in a single ended design the PSU sag is constant and therefore won't change the dynamics as much as with PP, most of the people use the SS module.
Chopsticking may help with the wiring issues, and in this stage the knowledge and application of electrical safety procedures come in handy.
It's best to try one change at a time, in order to be able to find out what caused the hum in the first place.
Regards
Sam