You could just make a spherical vessel and put it at the position of the sun. The planets can't be turned inside out.
still, textures would be absolutely frickin huge if you want to see more than one pixel per a few billion km^2. You'd have to program some kind of mip-mapping, and texture generating and... oh wait, this starts to sounds like Orulex and LibProcTer! maybe you could ask Artlav or CJP for an inverted version, that should do the trick nicely.
Actually, at one point I accidentally had an 'inverted' version of earth, with the continents and oceans on the inside

. I fixed it, but it should be easy to 'unfix' it.
libProcTer is quite scale independent, but OrbiterProcTer (the Orbiter version of ProcTer) isn't really designed for these scales. It proves that planetary-scale vessels are possible, but I have no idea whether a 'Dyson sphere' scale will give problems in Orbiter. You can test this even without a special DLL, by simply making a simple mesh of that size and combine it with a generic vessel DLL.
If it doesn't work, I can think of a way to work around the size limitation, but OrbiterProcTer doesn't use it, and AFAIK neither does Orulex. It simply isn't needed when working with normal planets.
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The idea of a Dyson sphere is not to keep all heat inside: the idea is to keep
useful heat inside, until it is fully used. It radiates away all the heat it receives, but it does so at a temperature which is not much more than the cosmic background radiation. So, on the inside the radiation is UV, visible light and infrared, and on the outside it is far infrared and microwave radiation.