Mass-produced vehicles of that era were built on assembly lines with hard tooling (think gigantic 500 ton presses to shape thousands of identical components) and a certain degree of loose-tolerance hand-work (riveting, welding, machining, etc) with materials that have long gone out of style (wooden structures, fabric-covered wings, etc). So if you want something constructed in a really historically accurate manner it'd be difficult. But if you were happy with a CNC-machined duplicate and modern materials/construction techniques substituted, probably not that big a deal.

Another issue is even if you do pull that off, the institutional knowledge hasn't always been preserved - you could build yourself a Norden bombsight straight from the blueprints then be baffled when it doesn't work and you need a 90 year old WWII vet to tweak it for you. There are museums and enthusiast groups that actually have to deal with these issues nowadays when restoring WWII tanks & warplanes to running order.

If you wanted to be accurate? Yes. You'd need period-relevant tools because of the nature of how the tanks and aircraft were manufactured.

Particularly, the nature of mass production from the era. Stalin wasn't joking when he said quantity had a quality of it's own- every T-34 that ever rolled off a production floor, every B-17, ever P-51 Mustang, every M4 Sherman was different at some level from every other. You don't just make thousands of anything at the drop of a hat. An incredible amount of planning and research and methodology has to be developed to make it happen.

One of the biggest would have been the incorporation of auto-welders, which both dramatically reduced the investment of man hours into welding large pieces of metal, as well as reduced the amount of skill and training necessary. Basically either a large apparatus would move the object you were welding against the welder, or the object would be rigged to a Jig which you would then move the welding tool through. The work of a team of skilled welders could be done by one guy with minimal training thanks to this.

WW2 era aircraft would be much the same. Most modern aircraft at the time had either entirely forgone the usage of wood, or reduced it to the trim, but the reality still remained that the fasteners and methodology was simply different. Mercifully the most common type of fastener- the rivet- in aircraft hasn't changed much.

that might be a good question for /r/AskEngineers