Hmm, hull of CV-6 ran 770 x 83 x 26 draft, which--at 1:32 scale--would be 289" x 31" x 10" (round numbers); so a hull about 8 yards long, not quite a yard wide, and not quite a yard tall.
Flight deck is, what, 825 x 109' ? Which would be 310" (not quite 26') by 41" (3'-5").
Would not need a base so much as a boat trailer. Figure a stock Dilly trailer is 8' wide, a person would have room for a plane guard DD--a 1:32 Fletcher would be 140 x 15 x 15" or so.
Which makes me wonder if a person could blow-mold a 0.5mil mylar wildcat powered by a servo motor . . .