Thanks everyone for your thoughts and suggestions.
Annie: Catherine Sinclair was around 37 when Charles junior was born. If Charles senior was from Rothiesholm then I think there would be some other evidence of him existing in Orkney at some point. Campbell's not an Orkney name, and there aren't a lot of them. There are only 3 Campbell baptisms on Stronsay listed on Walt Cursiter's site (has all OPR indexes for Orkney), none named Charles and baptism records go back to 1745. The only Charles Campbell on Orkney census records is the son.
I don't know for sure where the Charles who was born in 1816 and married in 1839 was in 1841. Freecen has a Charles Campbell, Cooper of the right age to be born in 1816 with a Margaret Campbell in Greenock but they're listed as born Renfrewshire. So that's either a mistake or it's different people. In 1851 in Greenock there's a Charles Campbell, general labourer, wife Margaret, both born Bute, Rothesay.
Interesting you think you saw another post about a child in Orkney with an absent father from Rothesay. Maybe the arrival of the herring industry resulted in a rush of illegitimate births every year!
Don: I spent a lot of time looking into the possibility that Charles Campbell sr was a cousin or some other relative of Catherine Sinclair's mother Catherine Campbell and couldn't find any connections. That was before I found (last summer) the baptism record that mentioned Rothesay (the baptism on Scotland's people is different. There seems to be a book of baptisms from the Kirkwall Free Church that's only in the library in Kirkwall and hasn't been put onto Scotland's people or the IGI). One of the trees you saw on the OFHS is very probably one I did.
On the 1841 census Nancy and Betsy Sinclair are actually the neighbouring household. They still could be related though.
Skoosh, interesting that coopers moved with the herring fleet. Do you know if there are any records which show which years herring were scarce in the Clyde and people moved to different areas?