If I don't want to shave peach fuzz hair on my cheeks for laser hair removal session, is it pointless to do LHR on cheeks then?

The reason hair has to be shaven before laser hair removal is the laser is attracted to the pigment of the hair.  If there is hair above the skin not only are you at a higher risk for a burn on the surface of the skin, the laser will not penetrate below the skin to kill the follice.  If the laser does not reach the hair follicle you will not have a successful result.  Also, if the hairs are very thin and don't have much pigment the laser treatments will not be effective.  

Hello,  First and foremost, the hair being treated must have pigment in it in order for the laser to see the follicle and destroy it.  Laser hair removal will not be effective for the white vellus hairs on your cheeks. (peach fuzz) Shaving your face will not make the hair grow back darker and thinker.  The purpose of shaving the hair prior to treatment is so that the heat is absorbed deep into the root of the follicle in order to destroy the follicle.  When the follicles are long, energy is wasted on the length of the follicle and also can cause smoke in the room.  Good Luck!