Heidi, I was recently doing a bit of research and came across a ship called 'Connivum' which I assume might be the same vessel but with a typographical error in the paper I was reading!
There is no mention of your relative but the captain in around 1846 (providing it is the same vessel) was John Parry and he was using the ship to carry building materials into Llandudno for some of the early hotels.
Captain Parry was master of 'Connivum' until around 1855 when he, and a syndicate of local businessmen, had the 'General Havelock' built with Parry at the helm.