We get lots of light wind days here too. Over the years I have had, or currently have, the following for lighter winds:
Nobile XTR. This was a 2007 143x48 I think. Was OK in lighter winds but with my 115kg frame it struggled in anything below 14 kts.
Spleene Monster Door 164x50. This was a great board for light winds / flat water at the time (2008) but upgraded later to Flydoor which was in a different league. I'm sure the newer Doors will be better.
Flydoor XL. This was version 3 (2011) was much lighter than the old Spleene and is still my goto in flat water and lighter winds. It feels much smaller than it is and is so comfortable and usable.
Sector 60. I have a V2, a few years old now but this is probably the ultimate for lighter winds, but you do need to learn how to handle a directional and those fins are so long they are a liability when you are in shallow water, in weeds, or on the beach.
Slayer 58 V2. Also a directional, great in light winds, almost as capable as the Sector in trucking upwind, but also ok in chop and waves. Wide and stable - great for learning strapless.
Mako King. Brilliant board in chop and rough conditions. Not as good getting upwind as the Flydoor in really light winds, but lovely to use, very smooth.
I haven't tried the Litewave TT or the North Nugget directional which sounds great.