I want to set up a business entity where I (CEO &/or sole owner) can sign non-competes on behalf of my business and not be personally bound to the non-compete. What's the right legal business entity for this requirement?
What matters is (1) who is party to the non-compete and (2) did the correct party sign correctly. Usually the first sentence of a non-compete (or any agreement) sets out who the parties are. Those same parties should be listed by name (whether individuals or business entities) on the signature page. And then the actual ink or e-sig should be applied by someone who is authorized to sign for that party (for an individual - the individual, for a business entity, an officer or other authorized person). If the business entity is the party to the agreement, and listed on the signature page, the authorized person who applies ink or e-sig to the document does not agree to anything by doing so.
Note all of this is assuming you are trying to document, in good faith, a real agreement between two parties. If you have setup this entity for the purpose of tricking people into thinking that you owe them a non-compete obligation when, by the way the agreement is signed you don't - well that's not going to work - save yourself the hassle and just take the chance that the counterparty doesn't go after you for violating your non-compete - most states frown on those anyway.
You should ignore the fact that you are the sole owner of the LLC. Instead look at it as the LLC signing the NDA, and an arbitrary person (in this case, the sole owner of the LLC, but that is pure coincidence) having the knowledge needed to breach the NDA.
The LLC signs, the LLC is bound. However, at this point it is the duty of the LLC not to give the covered information to anyone, and if it is given to someone (like the sole owner, or an employee needing to know the covered information to do his job), to make sure that the person will not breach the NDA.
So what you plan isn't going to work. You will be personally bound by the NDA, not because the LLC signing binds you personally (it doesn't), but because the LLC by signing will have the obligation to bind you personally or they will already be in breach of the NDA.