Do dismantle it for cleaning. You won't get the dirt out of the pivot holes otherwise. If you're not familiar with clocks take photos at stages so that you can see how it goes back together and remember to let the springs down carefully by releasing the ratchet while controlling the spring with the winding key. Don't try removing the springs from their barrels unless you are sure of what you're doing. There is a lot of energy stored in them.
Use clock cleaning fluid and clock oil from a supplier such as Meadows and Passemore or Cousins. The proper cleaning fluid will not only remove old oil and dirt but also the tarnish on brass. Finish cleaning the pivot holes with fine wooden pegs.
Russell