Fat pegs give coarse tuning and may leave no space to pass string under. Bushings(boxwood),pegs,peg_shavers,reamers etc. are available from companies such as Touchstone in Surrey, U.K. A good violin should go to a good luthier with correct tools. A lower quality violin will not repay the cost of above items and time. Only attempt this if you are a competent craftsman.
Alan G.
October 2016