Marine Recon would not have been used for a mission like this. While they are badass, this type of mission is exactly what ST6 and Delta Force were formed for.
As for The SEALs being chosen over Delta, I can think of a few possible reasons. It's possible Delta was just busy with other things or there is some sort of rotation for these types of missions and it was just ST6's turn. It's also very possible that Delta did take part in the raid, but because they "don't exist" they'll never be mentioned along side the SEALs (I suspect ISA had a hand in this as well, but they don't exist officially either).
The other (more outlandish) reason Delta might not have gotten the call I'd because of General McCrystal. Before he was the commander in Afghanistan, he was running Delta. After of what happened between him and Obama, maybe the administration decided to slight Delta and go with ST6.