Cool air falls and hot air rises.
If the AC unit is above the studio then ducting it through insulated flexible ductwork will do the trick to the ceiling space where the hotter air is. The insulated ducting will reduce condensation, and reduce noise.
Rember that noise will be reduced for every change in direction of the duct.
You must be certian that the air velocity comming out of the diffuser is a couple of hundred feet/min. to reduce air noise across the grill. Have an adjustible volume damper installed upstream of the register. Dampers create noise. The damper upstream will do the job of controlling the required air volume to the space, without creating the noise at the diffuser.
An in-line silencer can also be purchased and installed near the fan (for central type systems)to reduce unwanted fan noise, but the duct will need to be expanded at that point to reduce pressure drop across the silencer.
If you use metal ductwork, installing hard fiberglass insulation (glued to the inner walls)inside the duct will also reduce fan noise. A lot of comercial office buildings do this. Usually they place this insulating board in all changes of duct direction and at "Tee" connections.
Hope this helps a little.