Padding is about level. not about noise. If you can adjust your gain so the signal does not clip in the peaks, you should not pad it.
Unpadding should not add noise to your signal. Padding just makes the noise more quiet as much as the signal, so it maybe that seems to happen, but normally it doesn't. Just open the Gain to get the right Level again and you will have your noise back ;)
Maybe you should use a DI Box with Hi-Z Input for your guitar, this depends on the pickups you use, but would also give the possibility to remove humming noises from ground loops which may happen when connecting directly.
As well, you should check if the noise comes from your guitar Setup. Maybe you just have a noisy, badly insulated cable. Keep Guitar and Cable as far as possible from any devices emitting electromagnetic disturbances. That includes all electric Motors, some kinds of Lamps, Radios, WLAN Access Points, even fridges or dishwashers can cause noise.
You also might get some noise over the power line - there exist filters to prevent this, but those aren't cheap if you want them to really work.
Oh, and beware: NEVER EVER cut off or insulate any ground pins or safety contacts from your Power Cords to prevent humming or noise. It is life dangerous to do that! A single blank piece on your cable might be enough to toast you then! Instead, always use the ground lift switch of DI Boxes to stop ground loops.