Lawman
Photos would help. In any case, unless the wood is badly split at a "strategic" part such as around the pistol grip, which is apparently not the case, I would have the stock professionally refinished i.e. wood cleaning, dings & dongs repaired, checkering refreshed and new oil polish. If your existing stock is in good working condition, having a new bespoke stock made won't IMHO make any sense unless, for example, you would require a longer length of pull, and the cost for this new made-to-measure stock would exceed the rifle's value.
The (lucky) owner of a classic Ford Mustang with dented bodywork and paint in poor condition would have the car restored to its former glory so why not offering that "face lifting" to your faithful M.1903?
Louis