OK, first things first.
Are you asking about oil for the compressor, or the engine that drives it? (or do they share a sump?)
Engine? GC in the winter. Any dino HDEO or a straight weight in the summer. There's no need for a lot of fancy anti-corrosion oils since it's in constant use. You'll be changing the oil every week or two, no sense in breaking the bank. Furthermore, the GC may be a waste winter or not since it sounds like you start it once a day and leave it run. If you want extended OCIs go with something like Amsoil ACD or ASE (no VIIs, heavy on the addpack)
Compressor? That will be where non-detergent is required. If they share a sump you have a conundrum on your hands. Air compressors shouldn't use detergent oil as it can gum up the valves. If they don't share a sump, Amsoil makes a couple of nice oils you could probably run a high number of hours on between changes. I don't know what weight you need so it's tough to make a call.
My 1-2HP direct-drive compressor indicated that *IF* proper compressor oil couldn't be found a couple of select syn motor oils could be used in the compressor. These were M1 5W30 and Chevron syn 5W30 IIRC. Maybe, possibly, perhaps in the case of a shared sump you might be able to find an oil that will protect the engine far better than ND without destroying the compressor.