I have looked at the IGI again and I can see the 1725 marriage you mention and the four children baptised thereafter. I still cannot locate the 1703 baptism of Thomas that you mention
From the Ripon registers I can find the marriage of a Thomas Dixon and Anne Terry both of Sharow on 19 May 1699
There is then a baptiem of a daughter Elizabeth to a Thomas Dixon of Sharow on 2 April 1700.
Finally there is a death of a Thomas Dixon, yeoman of Sharrow (sic), on 18 April 1702. Don’t know if this is the Thomas who marries Anne Terry or another one
(I also looked under the name Dickson)
Sharow is just to the east of Ripon, and is 8 miles from Bishop Thornton
I understand that findmypast.co.uk are transcribing Yorkshire parish records to be online next year or shortly thereafter, so if all else fails that is a possible source for the future.