I've never needed to bath any of my piggies (including my long furred ones,) so I can't give a suggestion on what shampoo would be good, but I wouldn't use something formulated for puppies, so I would skip that Earthbath one. As Piggies&buns said, I'd just use plain water for most hygiene needs.
On the occasion that one of my piggy needed a foot cleaned, I'd just use a warm, damp paper towel and gentle soften and extract the clump of poo. (Poo dowsed with water can get soft enough to get between toes and would get caught in the front foot of my piggy with an extra toe.)
Before I switched my long furred piggy to fleece, the ends of the fur near her rump sometimes got a bit icky (particularly if she shoved the litter out of the corner before piddling

). I would comb out any tangles (routine) and clip off the ends that were too icky. Again, a warm, damp cloth can help if it's not something that warrants clipping but isn't quite clean either. Some piggy owners will clip fur short to reduce combing; I've been fortunate enough to have a piggy that is relatively cooperative, at least for combing. (Grooming = okay; looking in mouth = not okay ... cue screaming and peeing on vet.)
Just make sure to keep everything warm and free of drafts until fully dry if wetting piggy's fur (or foot.)