Several parts of your question raises red flags about whether you know what you are doing or not.
LLC does not have a director.
LLC does not have an shareholders.
Off shore from where?
Raise capital from whom?
Brokerage governed by what authority?
I suggest you think smarter by hiring a lawyer to go through some of these most rudimentary items BEFORE you start anything.
Good luck. Such a new business can have great potential for you if you start right.
If you're starting out in building a hedge fund business, the main reason why you'd want to be in a tax neutral jurisdiction is to gain the pre-tax benefits of enhanced performance and whatever trading you're doing (long term v. short term capital gains). You might wish to start in a tax neutral jurisdiction due to restrictions on margin in the US and what markets you can access for trading as well. You also need to consider where your desired investors may be. Some places are looked upon more favorably than others for various reasons (tax treaties, etc). But if these considerations aren't primary drivers, then it may make sense to simply create a US fund.
The registration issues as to whether you need to be licensed, etc. depend on several factors that would require extensive discussion, not to mention how, when and where your fund might be marketed and domiciled.
Remember, however, that hedge funds that seek to retain the assets of institutional investors require three things, those being (a) an auditor, (b) a law firm to prepare the PPM and who will put their name on it, and (c) a fund administrator. For start-ups, there are actually platforms that provide these moving parts. Many managers actually prefer the platform model to the individual fund model. These platforms are available through providers in most tax-neutral jurisdictions of choice, including Malta and others in Europe.
In short - don't try this without professional help and a real business plan in which you are confident.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.