Only birth registration I can see in GRO births index via FreeBMD for an Arthur Davison born 1861-1863, Co. Durham is:
Davison Arthur Q3 1863, Stockton 10a 34 , as Wolviston was in the Stockton Registration District it looks like the baptism I found is the right one - even though the vicar added in an extra 'd' to the surname.
If his Dad 'was' James and a shoemaker, then this looks like the family in 1871
RG10. Piece 4899, Page 27 living in Wolviston
Head James DAVISON, age 53, Occ Shoemaker, born Wolviston
Wife Mary DAVISON, age 41, born Yorkshire, Faceby
Son Frederick G, age 20, occ shoemaker
Son Edmund J, age 19, occ shoemaker
Son Henry C (?) age 14
Daughter Margaret A , age 11
Son Alfred age 9
Son Arthur, age 7
Daughter Edith I, age 3 All children born Wolviston
1881 census RG11 Piece 4893, Folio 90, Page 8 still in Wolviston
Head James DAVISON, age 63, shoemaker (says he is married but wife not listed in household)
Son Edmund J, age 29, shoemaker
daughter Margaret A, age 21
Son Arthur, age 17 occ ? BSmith
Daughter Edith I, age 13
1891 census RG12, Piece 4017, Folio 62, page 8
Arthur living in Normanby (Ecclesiastical Parish of Eston) listed as a lodger in the house of Walter JOLLY, age 29, occ Blacksmith & Gas Fitter
1901 census in Milton, as given to you on the Kent board
1922 GRO deaths index via Free BMD
DAVISON Arthur Q2 1922 Stockton 10a 88
1922 Probate Calendar England & Wales
Davison Arthur of Lax Terrace, Wolviston county Durham died 29 Apr 1922 Probate London 12 May to Lilian Agnes Davison spinster. Effects £179
Of course, if the marriage cert doesn't say his Dad is James, then its back to the drawing board :-) but I would suggest that if you don't have access to census info, go to your library and use their pcs to look at the 1911 census which indicates that the above census info 'is' correct.
Sorry, but we aren't allowed to post details of the 1911 or I could tell you why I think it confirms it :-)
Boo