I've seen the Corsair fly, and it's pretty good. The Zero is smaller, but I don't know much about it.
The key thing about the P-47N is the wing area, and to a lesser extent, the wingspan. The P-47N is the largest of those kits, so it handles the weight best and turns tightest.
I wouldn't bother sheeting with wood. Too fragile, though there are some kits out there with Obichei (sp) sheeted wings. Ive also seen them get blown in half in the air, so I wouldn't go that way.
When I did my P-47's, I also replaced the wing spars with 1/8" fiberglass rods. That allows the wing to take a hell of a hit and stay together. Wing strength is important, and those bends in the corsair wing make it hard to build light and strong.
For scale combat planes, I always paint over the tape. You can scuff it up with steel wool or sand paper, then paint. Using "plastic primer" helps a lot.
For heat-shrink, you need low temp. Monokote is right out. Ultracote (best, imho), towercote and econokote are useable, but keep the iron as cold as you can, and move it often. Otherwise you melt the foam.
The plane below is a tape job. It also just got hammered, note the missing aileron linkage, and all the prop cuts in the belly and all the way through the wing. Also the missing vertical stab. This plane was later repaired and is still flying. (the fuse for sure, the wing, I'm pretty sure I fixed, that damage isn't bad) (ok, it's not flying right now. It was hammered again in Detroit, and is on the bench at the moment with more prop cuts to the fuse). The big pink areas on the LE's are from earlier mid-airs that put dents in the wing and scrubbed off parts of the paint, but didn't disable the plane.
Oh, that's another reason to build multiple of the same airplane rather than multiple different airplanes. More than once I've swapped parts, a wing here, a fuse there, to get a flyable plane up. In this pic, the wing is done for the contest, but that fuse is field-repairable if necessary. (I didn't need to, but those foam cuts are non-critical on that plane, and I always have spare tail parts around)
