Will skill levels transfer over whenever sims are aged up? (help needed)

When you move Sims out, you can choose to play them in their own household, or mark the household as unplayed, in which case they will become like NPCs. There's a plumbob you can click on their family portrait in the household management screen if you want to do that. You can also just leave them marked as played; it sounds like you have aging off, so unless you have aging on for unplayed Sims the effect would be pretty much the same.