One of the problems today is that the quality of plywood being offered is uncertain at best. I have bought excellant plywood at the "Big Box" building centers...and some terrible stuff! I've had better luck buying from local lumber yards, but even then, at times, there has been inter defects in the plywood.
If I was going to build such a trailer, I use marine plywood everyplace that I could, with quality hardwood for the inter-bracings. Also tape all the seams, where the plywood edges meets plywood edges, with fiberglass tape, then cover the entire trailer exterial with 6 oz fiberglass cloth and epoxy!
It should never leak...but, the cost would be very high, and the trailer would be quite heavy!
So...I'm still hoping someday to find that "dusty old Compact Junior or ll in a barn somewhere" where the owner pays me to haul it off!