I have checked the directories i have for Snoops, and for thje period 1862 - 1949 get the following . Note that the year given is the year directory is published, and probably refers to year before. Also, have transcribed what is written ie. if it said Snooks rather than snoo[ps that is what I've written. Am not too sure as to whether the Samuel Snoop of 1862 is the same as referred to in your post, as he would only be 14, but they did start early then !
1862 Samuel Snook, coal dealer,31 Stone yard, Deritend
1876 & 78 George Snook, furniture remover 39 Stone yard
1878 - 1883 Mark Snook, coal dealer, Victoria Road,Aston park
1880 -1888 George Snook, furniture remover, 7 Chapel house st
1883 Samuel Snook ,shopkeeper,Albion Rd, Sparkhill
1884 Samuel Snook, haulier, 79 Warwick St
1888 & 90 George Snook, thimble maker, Floodgate St
1888 ` Matthew Snook,beer retailer, 146 Berners St
1888 William Snook, Old Stone Cross Pub, 60 Dale end
1892 &1895 George Snook, Thimble and hair pin maker, Floodgate St
1892 Matthew Martin Snook,beer retailer, 21 New St, Aston new town
1892 George Snooks, private addr 195 Coventry Road
1892 - 1904 Isaiah Snooks, shopkeeper, 90 Greenway St
1895 George Snook, private addr 212 Green Lane
1896 - 1900 William Snook, private addr 110 Alston St
1896 – 1900 George Snooks, private addr St Mary’s Road,Stechford
1899 - 1921 George Snook & Co, Thimble and hair pin maker, Floodgate St
1899 & 1900 Mrs Harriette Snook,shopkeeper,139 Wilton st
1899 & 1900 George Henry Snooks, wardrobe dealer, 188 Icknield Port road
1904 George Snooks, private addr. 20 Abbotsford Road, sparkbrook
1904 James Snook, greengrocer, 20 Tower road
1908 George Snook, private addr.92 Gladstone road,Sparkbrook
1908 Herbert Edward Snook, 220 Mary st, Balsall Heath
1908 James Snook & Co, merchants, 20 Cannon St
1912 James Snook Private addr. 11 Dora road,smallheath
1912 Herbert Edward Snook, cab proprietor ,220 Mary st, Balsall Heath
1913 & 1921 Herbert Edward Snook private addr 11 Mossfield Road, Kingsheath
1913 - 1933 James Snook Private addr 94 Gladstone road.Sparkbrook
1921 Mrs Dorothy Snook, greengrocer,271 Icknield port road
1932 & 1933 George Snook, private addr.57 Addison road,kings Heath
1932& 1933 George William Snook, private addr. 24 Tennyson road smallheath
1932 & 1933 Mrs Lilian M Snook, private addr.1609 Stratford road hall green
1932 & 1933 Mrs Amy Snook, 11 mossfield road,kings heath
1932 & 1933 John Snook, coal dealer, 32 Regent Park road smallheath
1940 - 1949 Frederick Snook Private addr. 98 Corisande road, Selly oak
1940 - 1949 Harry Snook Private addr. 16 Corisande road, Selly oak
1940 -1944 Thomas Herbert Snook, Private addr 254Selly oak road,kings Norton
1940 - 1949 Walter Thomas Snook, private addr. 48 kingstanding road
1940 -1944 William Samuel,private addr, 62 Bankes road, small heath
1943 & 1944 Bert Snook, private addr. 58 Rymond road
1943 - 1949 Ernest Donald , private addr. 150 Green acres rd kings Norton
1943 - 1949 Isaiah Snook. private addr ,511 Kingstanding road
1944 Ernest Donald Snook.Private addr. 150 Green Acres Road, kings Norton
1949 Thomas Snook, Private addr . 352 Old Walsall road,Great Barr
1949 William Snook, Private addr.69 Hillaries Road erdington
Mike