Although they've been doing it for way too long, Congress, the legislative branch, cannot constitutionally commandeer or delegate its rights and responsibility to another branch, in this case, the DOJ, part of the executive branch. It denies the clear constitutional intent of separation of powers.
The issue is not that a "special counsel" must be an expressed enumerated power - there are lots of constitutional federal acts and personnel not expressed as an enumeration of power - only that they are "necessary and proper" (N&P) to carry out those enumerated powers. This "special counsel" is not one of those N&P acts IMO because among other things it violates separation of powers and also allows Congress to do what they do best - skirt the politically-volatile issue issue and leave it to some unelected someone in another branch.
The proof of these extra/un-constitutional federal moves is in the pudding in the extraordinary conflict of interest that immediately arises when the DOJ investigates itself.
I think you are mistaken delegate with relinquish. I believe that Congress can decide to and exercise its action through action and inaction. That's a negative affirmation interpretation. If Congress fails to act, then they are in effect delegating authority to the executive branch.
However in the end Congress owns the product and use its power to nullify and fix.