It's difficult to be precise because it depends what centre stone you go for (and of course the metal of the ring). However, if you're worried about the pearls specifically, you do need to take care. Pearls are generally either glued onto a piece OR there is a metal peg set into the mounting of the ring, a glue is then added to the peg and the pearl is slid onto it, holding it in place. Of course this means that glue can break down over time so avoiding water is important.
You can buy specialist cleaning cloths for pearls which would be best for the pearls and then use a damp (not wet) toothbrush with a tiny amount of washing up liquid for the rest of the ring - taking care to avoid the pearls and not getting them soaked in water. Hope that helps.
When it comes to something mixed like this, look for the most delicate item in the ring and clean only the max recommended for it. In this case, treat it just the same as any pearl item. Do not soak the ring, avoid any chemicals and cleansers, and only clean it by dabbing it with a soft damp cloth.