First, I'm assuming that you’re a CSG ship and not an independent steamer. If your independent, then it will be pretty much ops as you're used to.
If you're part of the CSG, then the CO of the HSM squadron will be on the carrier and he'll work for CAG. However, when the det is embarked, they'll be a DESRON asset to employ. (CAG will own all the maintenance headaches, but DESRON will employ). I wouldn't think you'll have much difference in how/when you can employ the Det, it will be based upon the personalities of the CAG and DESRON as to how tight they want to micromanage (much like today....)
You still should have the same PUK since that is considered a ship asset. The Det will be roughly the same size and you may get a one bird or two bird det.
For Operations, once the Det embarks, they will answer to you, but their CO is in theater, so if there are issues regarding tasking, they can call home to mom a whole lot easier.
From your view point, if you have an issue with a member of the Det, it will be a lot easier to change them out, since the Carrier will have a 4+ bird det embarked with the squadrons front office.
Of course this could all change...