I did look for a christening on all of the free sites, and on the Wolverhampton parishes site as well. Both for George Haycock and George Whitehouse/Whitehead.
Naturally I might have overlooked something
Is this one of the sites you have looked at ?
http://www.wolverhamptonhistory.org.uk/resources/indexesdidn’t come across a baptisms for George Haycock/Whitehouse/Whitehead b1863
or Thomas (John) b1843
From the info. John & Susan baptized their children at
St Mary's Wolverhampton and they married there too - you probably have all the details below but you never know......
Marriage St Mary 28 Jan 1850
John
HEYCOCK f/a Smith Stafford Street F John Heycock Gardener Susan DICKSON
Sophia HAYCOCK d of John & Susan 17 Nov 1850 Stafford Street Whitesmith
Sophia Haycock Dec 1850 Wolverhampton (FreeBMD)
Alfred HEYCOCK s of John & Susan 25 Jul 1852 Stafford Street Whitesmith
Alfred Haycock Sep 1852 Wolverhampton
Alfred Haycock Sep 1852 Wolverhampton (death) (FreeBMD)
Solomon HEYCOCK s of John & Susan 30 Nov 1853 Falkland Street Blacksmith
Samuel Solomon Haycock Oct 1853 Wolverhampton
Samuel Solomon Haycock Dec 1853 Wolverhampton (death) (FreeBMD)
Frederick HAYCOCK s of John & Susan 5 Aug 1857 Falkland Street Blacksmith
Frederick HAYCOCKS Sep 1857 Wolverhampton FreeBMD)
Joseph HAYCOCK s of John & Susan 26 Dec 1858 Falkland Street Blacksmith
(FreeBMD has a birth entry Dec 1855 Wolverhampton Joseph Haycock perhaps he as baptized at a later date)
This looks to be the marriage of son Joseph although his year of birth differs from baptism date
St Mary Wolverhampton 24 May 1874
Joseph HAYCOCK 21 bach. Blacksmith North Road John Haycock Blacksmith Fanny WALTON
1881c Joseph & Fanny HAYCOCK living 100 North Street, occ Blacksmith with children
for info. here's one of John & Emily's children baptized
St John’s WolverhamptonSusan Florence HAYCOCKS dau.of John & Emma 13 Apr 1868 Drayton Street Blacksmith
Susan Florence Haycock Mar 1868 Wolverhampton (FreeBMD)
If your George’s birth was registered is it possible his pob is not Wolverhampton and he was born elsewhere in Staffordshire or maybe some else