The smog check program will be administered according to the engine year of your C10. In other words, after replacing the current engine with a 2003 Chevy Diesel, the DMV will require your C10 receive biennial smog inspections; as 1998 and newer diesel trucks require smog checks.
The initial smog inspection after you swap the engine will need to be administered by a California Smog Check Referee. They will ensure the swap was done properly, all the new emission components (those which belong to the 2003 engine) are present and functioning. After passing the referee's smog inspection, a blue tag will be placed on your vehicle indicating it has received a legal engine change. Subsequent smog tests can be done at regular smog stations.