Is probably the brother of Cecil Cheesman who also served in the South African War.
Changed surname from 'Cheeseman' to Cheesman'.
The service record uses both 'Cheeseman' and 'Cheesman', though it appears that Walter himself signs himeself as 'Cheesman'. See also community contributions under Cecil Cheesman's page (linked above) which suggest his family name should probably be spelt 'Cheesman'.
Download Walter Cheesman's service record here (Archway)
Community contributions