Oak Park is the large cemetery in the Chandler area.There is a tombstone for F. M. Shaw, b. 27 December 1841, died 4 April 1920.Could this be your ancestor?
There are several Shaws buried there including a Mary R. Shaw, b. 15 Oct. 1842, d. 2 Sept. 1904.There is no indication whether or not this is his wife.
If you think this is your Francis M. Shaw, I'd suggest going to the Oklahoma part of genforum and posting a request for a lookup from the 1900 U. S. census looking for the name.Or, perhaps one of the Lincoln County lookup volunteers could help you.