It is hard to imangine that smart people in the other solar system won't figure things out. The physics of nuclear is mostly known, which is why Iran and North Korea can have nuclear programs despite efforts to stop it. Anything secret that is exported to a different solar system is reverse engineerable.

The first colonists will of course need to bring stuff with them, but it doesn't make sense to assume they won't plan on building most of what they need once they get there. It is a lot easier to setup manufacturing when you don't have to invent the assembly line.

I can maybe see trade of one of a kind things. It hard to believe the Mona Lisa would ever leave earth, but that type of thing where the original is the thing might be worth it. Not enough to sustain trade though, the time line is far too long.