You are correct that you need a larger needle/tip combination. About 20 years ago, before I started turning and was doing flatwork WW, I decided to up my finishing capabilities. I wanted a gun that could spray oil and water based finishes. I tried several under $100 guns, and none could appropriately atomize WB finishes. All of them could spray OB just fine, as OB finishes can be thinned pretty much without worry. WB cannot - usually about 10% max. WB is much more difficult to get a nice finish "off the gun".
There are 2 design aspects with spray guns - 1. tip/needle size, 2. Air Cap design. Even with a larger tip/needle to get enough flow, air cap design can limit atomization. You need fine atomization without hi air cap pressure (which generates hi velocity and a lot of overspray). I finally purchased a nice gun, and things fell into place. I have the one below with the tip/needle sizes for wood working. I think I got it from Finish Systems. Scroll down and read their blog - they have very good spraying information. A also have the 3M PPS cup system, much easier to use vs a standard cup.
The C.A. Technologies CPR (CAT Pressure Reduced) gravity feed spray guns combine the transfer efficiency of HVLP with the speed and finish quality of conventional air spray. The spray gun comes equipped with an HVLP and Pressure Reduced (Compliant) air cap allowing the user to switch between the...
www.finishsystems.com
I will say that I do not use WB on turnings anymore. If I spray a turning it's typically OB lacquer, and just about any cheap spray gun can be made to work by thinning the lacquer to a good spray pattern. The WB finishes just do not look as good as OB to me.