Search for "model plywood" online, and you'll get plenty of hits. The model airplane crowd use a lot of it (a fellow sailor likes his scratch built model planes).
I can get plywood down to 0.4mm thickness but I have to get it from Germany - I use this company for those people outside of the USA: http://shoptest.arkowood-shop.com/Hoelzer/Sperrholz/Flugzeugsperrholz-Birke/ I'm sure it will be available in the States - as Mummichog says, the aircraft modellers will be using it.
Which reminds me, I need to get a few sheets of 0.4mm ply to make a scale replica of my Chesapeake 17LT and possibly the sail rig too this winter. :) Earlier this year I helped a class at the local primary school make about 24 model kayaks. Nick Schade kindly let me use his Ganymede kayak plans - just 6 pieces of plywood, some matchsticks and telephone wire for the stitches.Here's one of them
Whilst not difficult to make - the plywood can be cut with scissors - I can tell you that coaming rings are very tricky!
We're stocking modeling plywood in 1/32", 1/16", 3/32", and 1/8" in order to accurately scale the thickness and bending characteristics of full-scale marine plywood.
It's been tricky to find that plywood in the requisite quality and quantity! We hadn't planned to sell the modeling plywood ala carte but maybe if there's enough demand...
Having the stuff laying around, along with a big laser cutter, has been cool for my extracurricular hobby, designing and building RC airplanes:
(CLC is definitely not getting into aircraft, before you start in on me.)