Is this the sort of davit you had in mind? On my model it was used to move the accommodation ladder seen stowed on the hatch cover of No.3 hold into position when the ship is alongside. It is known as a radial davit and is easily made, as you intimated by tapering a length of brass rod in a lathe or even an electric drill. The tapered rod should then be heated to temper it and then bent around a former of a suitable radius.
One of the best books about ship fittings is "A Ship Modelmakers Manual" by John Bowen. It was published in 1982 by Conway Maritime Press, is quite rare now but well worth purchasing if you can find a copy. James Pottinger has also just published a useful book "Model Ship Fittings".
Hope this helps, Chris