You only need a FINRA series exam if your employer is a registered Broker-dealer. Hedge funds are not typically BDs. Some prop firms are and some are not. The ones that are, typically require the SIE and 7, but some might require the 7 too.
A hedge fund trader traders the money of the LP and does not trade the client's money which would imply the owner of the account is the client. Those are called separately managed account (SMA) when the client is the owner of the account.
A CTA needs a series 3.
A hedge fund is a pooled asset not SMA. A CTA with a pooled Asset is either a CPO or an exempt CPO. A CPO will need a 3 and might need a 7 too as it might be considered the sale of a security.
A hedge fund that trades futures but is exempt, will likely not need a 3, only be an RIA.
You really need to look to a pro for some of this to get the best answer that takes into account your state laws + regulators.