If there is poop sticking to the bottom, but you say he is producing hard poops, it suggests the sticky poop around his bottom is caecotropes. These are mushy poops that the rabbit produces naturally and should eat directly from their bottom - this helps with digestion and is very important for rabbit health. If your rabbit is not eating those caecoptropes, there could be a few reasons:
If the diet is too high in protein and sugars (e.g. too many pellets/fruits) the gut is already overwhelmed and so won’t feel the need to eat the carcotropes. The rabbit diet should be 80% grass/hay, with some veggies and pellets just to supplement.
It also might be that he isn’t able to eat the caecotropes. If your rabbit is obese, or has painful joints, for example, then he won’t be able to bend down to eat the caecotropes and clean himself properly.
It is important to make sure you tackle this at the root cause to prevent it happening again. It’s also possible the mushy poops are diarrhoea, but as you say he is producing hard poops this seems less likely.
As for cleaning him, you could bathe just his bottom with some warm soapy water and a flannel, making sure to dry him very well with a towel afterwards.