Put some round butt grips (speed 6) on your square grip security six and see if they will affect the serial # issue. If not, merely scribe a line around the round grips on both sides of the frame and then preferably file, or CAREFULLY grind, away the excess butt frame material. Place the RB grips on the frame frequently so that you can determine when you have removed the correct amount of material. Note that the grip backstrap is somewhat rounded, so take care not to remove material to the extent that you end up with a flat backstrap. You might not like that.
Hopefully you are dealing with a SS version of the revolver. If so, merely smooth the site where the material was removed with various grades of emory cloth and then blend with scotch brite or similar product. If not SS you will obviously need to have the piece blued.
Not particularly difficult, but one should employ prudence, patience and a light hand in making the change if not particularly experienced in this type of metal modification..