Some information for you to chase up:
Free BMD information:
Marriages Jun 1902
Shelton Joseph Manchester 8d 284
Births Jun 1906
Shelton Joseph Manchester 8d 298
1901 Census:
Name Age Where Born Administrative County Civil Parish Occupation
Joseph Shelton 33 Lancs Manchester Manchester Manchester Plumber House
Joseph Shelton 52 Warwick Burton On Trent Manchester South Manchester Cooper
There are 47 matches for the surname Shelton in Manchester in 1901 & 92 matches for Sheldon in Manchester in 1901
Emily Warburton 15 Lancs Manchester Manchester Manchester Shirt Machinist
Emily Warburton 20 Lanc Manchester Lancashire Manchester Manchester Confectioners Assistant
Isabella Warburton 9 Lancs Manchester Manchester South Manchester
Isabella Warburton 28 Lancs Manchester Manchester Manchester
Isabella Warburton 56 Lancs Manchester Manchester Manchester Shopkeeper Grocery
There are 20 matches to a Thomas Warburton in the 1901 Census for that area
Edward Warburton 5 Lancs Manchester Manchester Sth Manchester
Edward Warburton 12 Lanc Manchester Manchester South Manchester
Edward Warburton 17 Lanc Manchester Manchester Manchester Letter Press Printer
I have also picked out some names to see if your Grandfather and his siblings were named after an older member of the family:
Name Age Where Born Administrative County Civil Parish Occupation
Walter Warburton 11 Lancs Manchester Manchester Manchester
Walter Warburton 28 Cheshire Macclesfield Manchester North Manchester Electric Car Washer
Francis Warburton 18 Lancs Manchester Manchester Manchester Sandwasher
Arthur Warburton 3 Lancs Manchester Manchester Manchester
Arthur Warburton 6 Lanc Manchester Manchester Manchester School
Arthur Warburton 22 Lancashire Manchester Manchester South Manchester Grocery Shop Assistant
Arthur Warburton 34 Lancs Manchester Manchester South Manchester Postman