The Imperial Yeomanry was created in the UK. One problem as you have discovered is that the Boer War medal roll only gives initials of forenames.
Also, how can you be sure he did not enlisted as plain Walter Webb? The attestation forms for the IY are in the National Archives. There were three W Webbs - but no Walters:
Webb, William 38542, Private 131st Coy., 29th Bn. I.Y.
Webb, William Harcourt 1120, L/Corporal 6th Coy., 4th Bn. I.Y.
Webb, William Thomas 24033, Trooper 67th Coy., 18th Bn. I.Y.
The forms for the CIV - City of London Imperial Volunteers have been lost. The only W Webb was WG Webb anyway
Other individual records - ie covering the Regulars and short term volunteers are no longer available in Kew, since they were put on Findmypast - or Ancestry if he served beyond 1913 without a break.
You may be better off ignoring the military angle and look for something in his local newspaper.
Ken
