A few questions?
Was James Arthur in the military (Canadian or British) when he died in 1943. He does not show up as Canadian war dead.
If he married in Hereford, you should be able to get a copy of his marriage certificate using information from Free BMD. You can search for marriage and death information but will have to do a search for the site as I am typing mainly from memory. I did a quick search for his death in Hereford in 1943 and didn't find anything.
I have found 2 possible fathers for James Arthur Smith.
Using the WW1 Attestation Papers and after doing a search of the 1911 census of the Prairie Provinces
I think the first one is the one you are looking for.
1911 Census/Saskatchewan/Battleford/32 Township 46
Smith, Arthur, boarder, single, b. April 1890, England, age 21, immigrated 1910
methodist, laborer on a ranch
in the household of Seigel and Emma Ricketts
TW47 Range 11 West of the 3rd Meridian (this would be in the vicinity of Shellbrook)
Found the Attestation Papers for him
Arthur Smith
Reg. #886449
Shellbrook, Saskatchewan
b. 8 April 1891, Otley, Yorkshire, England
office clerk
Next of Kin - Eleanor Smith, wife
enlisted 9 March 1916, Prince Albert, Sask.
The second possibility is
1911 Manitoba/Marquette Township 13
Arthur Smith
b. May 1890, imm 1911, labourer
in the household of Water McFarland
Attestation Papers
Arthur Albert Smith
Reg #2115703
b. may 1, 1890 Tottenham, London
Enlisted Oct 11, 1917, Winnipeg
He was a member of the Royal Canadian Legion, Shellbrook #111 for 53 years and died Dec 13, 1972
So that means 2 different Arthur Smith's were born 1890/91 and lived in Shellbrook at some point.
I checked the 1916 census and wasn't able to find Arthur, Eleanor or James but the new site at LAC isn't as user friendly as Automated Genealogy where you can look at many different spellings of names/dates of birth/etc. At the LAC site you have to put in specific names/places and dates of birth to bring anything up.
I went to the new census information for 1921 at Ancestry.ca and I checked one district for North Battleford that showed Shellbrook but didn't find anything. You may be more successful with the 1921 once the pages are indexed by name.
Some sites that could be helpful in your search are
www.wapitilibrary.cawww.shellbrook.netShellbrook Public Schools
110 1st St E
Shellbrook, SK S0J2E0
Shellbrook is a very small place so contacting the library may be a good option. They will have knowledge of cemeteries/newspapers, etc.
Births in Saskatchewan are subject to privacy laws and are only avialbe before 1913. As far as I can remember, marriages have not been transcribed as yet.
Hopefully, someone with more knowledge of Saskatchewan will pick up on this and be able to help you continue your research.