G'day from sunny Australia, Marc. Having built a Chesapeake 17LT earlier this year I feel qualified to answer this, so here goes - you should re-double your efforts to obtain 4mm marine ply for the hull and 3mm for the deck. Try the internet, kayak clubs and their members, etc., for info on sources.
If you build out of 6mm several things will happen: you may find difficulties with the ply taking up the correct shape of the hull, especially at the ends: you will NEVER get the 6mm to take up the heavy camber of the deck in front of the cockpit: and above all it will weigh a ton. Over and above all this, I think it would spoil the building experience for you, depriving you maybe of the joys of going on later to build other designs (the Chesapeake is a fine first choice).
If worst comes to worst, I'd be inclined to use carefully chosen exterior grade for both hull and deck, if you can get 4mm and 3mm respectively. At a pinch, 4mm for both would be OK, but it's a bit of a test of brute strength getting the deck ply to conform to the camber, despite the fact that 4mm is the recommended deck material. Most Chesapeake builders use 3mm for the deck - I did.
I know of many builders here who use exterior ply for S&G designs for many reasons - availability and cost being among them, and often they seem to be able to achieve a nice clear varnish finish anyway. If not, a paint job can often look just as nice on the hull with varnish on the deck (that was my choice, even with marine ply all round).
An alternative suggests itself since you are apparently an experienced woodworker - if after all attempts you cannot get the preferred marine ply, why not think about a strip-plank build? Usually I'd suggest first-time builders should get their hand in first with a stitch-and-glue craft, but your case seems a little different. It comes down to your confidence in your own abilities, I guess.
But stay away from that all-6mm barge!
Keep us posted, won't you?
Cheers...
Wordsmith