If you are lucky enough to buy a reformed cave then a chimney will probably be the last feature of the cave you think about when first walking through the door. For a semi reformed cave or a "wreck" then a chimney may need some thought.
You can of course choose any design you wish although my opinion is to remain with the flow, different villages do have different chimney designs. Building one yourself is quite easy, in our case a foundation was dug on the roof, filled with concrete and then bricked up to create the body. On top we placed a few more bricks inkeeping with local design and rendered the entire structure (no need to render the inside)
White chimneys stand out and look good, stone built structures are less dominent over the landscape but create that rustic touch.
Maybe a chimney suggests the trend inside a cave? A good well done structure looks great as will the rest of the dwelling inside and out. Something that resembles a half rendered dogs hind leg will not.