Hi Toban
I can't find John any where on the 1851 census, I see that Ann is a servant with a family.
The only burial record I can see for John Wild, is the one for Walsall St, and I think you have this.
I have Googled Walsall St and it is around the corner from Ward St, the age is a bit out but this not unusual, as the information is only as good as the informants knowledge, also his year of birth on the 1841 census may also be out, as they rounded up or down by 5 years
Here is the GRO ref for that burial
John Wild
July-Sept Qtr 1856
Reg Wolverhampton
Vol 6b
Page 229
The only other suggestion I can make, did he go to Australia as well
Marg