Hi,
I think you can discount the NIH or SIH as at this period prior to 1908 they were not in existence. The bandoleer is the clue here, it's one that would have been in use for the Boer War so I'd bet on an Imperial Yeomanry unit, by 1903 a leather bandoleer was in use and the SIY (formed in 1902, changed to SIH in 1908) used this as part of their uniform.
Using Kevins Asplins page here:
I found four Walter William's with surnames beginning with 'S' a long shot I know but then spelling is not our greatest asset.
Scott, Walter William Edward 25920, Private 53rd Coy., 11th Bn. I.Y.
Sharpe, Walter William 4284, Private 62nd Coy., 14th Bn. I.Y.
Smith, Walter William 34187, Sergeant 112th Coy., 11th Bn. I.Y.
Spratt, Walter William 30439, Private 34th Coy., 11th Bn. I.Y
There are 79 men with the forename Walter ...... Best match was
Slater, Walter 43452, Trooper* 33rd Bn. I.Y. (I'd put money on this one!!

)
The Imp Yeo records are available at Kew so if you look you'll know if this is your man or not

The foregoing is just another take on the question and my two pennies worth, also just wanted to quash the SIH angle..