Unless you book a private transfer/excursion, you will need to get an expensive taxi, or take the bus. I don't think you'll be wanting to pull luggage to the nearest Blue Lagoon bus stop from Skarfabakki, so maybe take a taxi to bus stop or bus terminal and go from there. I believe Blue Lagoon bus goes directly to KEF from the lagoon, so that should be easy to arrange, but you will have all your gear with you.
You are correct there are 2 harbours, the old one near the Harpa, and the new one that most large cruise ships use. (in opposite direction from the Harpa)
Maybe you meant taking a transfer/taxi to KEF, store luggage there, then make your way to Blue Lagoon, free of cumbersome bags.
Nothing's cheap in Iceland, just beautiful, including their people.