I was not suggesting that hiring a DM is a bad idea. A DM can help provide a comfort level, act as a guide, point cool stuff out, and help keep you safe.
What I was suggesting is that if weight and/or buoyancy is the only concern, those are skills a diver must develop, and a DM is not going to be a magical fix. The best place to figure out weight is likely in the pool. Get an empty tank (around 500psi), get in the water, and try to sink. If you sink like a rock, subtract weight, if you can't sink add weight. Use the same exposure protection/setup you will use in Coz. If renting gear, I suppose this becomes more of a problem, as you would have to rent at the pool, and the configuration may not be the same.
Once you get to Coz, add 6lbs to your belt/BC, and you should be fine in saltwater. If you are concerned about being under weighted, add 8lbs. Most new divers are NOT under weighted. When I did OW, my LDS gave me 28lbs, and as it turns out, I could have done it easily with 20lbs even as a newbie.
Buoyancy/trim is a bit more difficult. However attaining good buoyancy in salt water is generally easier than in fresh. If you are feet down, you can strap some lead to the top of the tank. If you are head down (rare), you could use ankle weights.
For a new diver having a private DM is a great idea. I just don't think one needs a DM for JUST figuring out weight or trim as that should be done to your best of ability before you arrive at an expensive dive destination. You want to arrive with good knowledge of your gear configuration. Cummerbunds/belts should be adjusted to size if necessary, hose routing should be correct and ready to go. Weighting, and weight placement should be for the most part a known quantity.
Adjustments can certainly be made upon arrival, and at the suggestion of a DM, but they should be minor. I think a shore dive to get things smooth is a great idea. If you are renting gear, I know that Christi for example spends some time at the shop making sure things fit before you go out on the boat. I would assume ALL shops do so as well.
You did not indicate where you are staying, or whom you are diving with? Finding a DM should be easy. I'd contact your hotel and/or Dive Op and discuss that with them.