I have found the parish records for St Mary, Chatham, Kent and the marriage register for that time period is here https://cityark.medway.gov.uk/Details/archive/110002242
and the record you are after is in P085-01-50(4). pdf in about page 32 of 67 BUT I am certain that Thomas surname is Bell or Ball in the record not Wood.
I am finding these files are opening very slowly and that may be my internet connection and the time of day/year but they do open eventually.
If you agree that the surname isn't Wood, then I would suggest that perhaps the marriage took place in or near Hull, given that's where the eldest children were born?
You are right that the census record does indicate children born in Yorkshire and Chatham and given both places were related to the sea, perhaps Thomas was a mariner or involved in trade/shipping somehow?