I don't think that the Honda EU3k gennys are designed to easily duct the exhaust outside either. If it was mine i would run it in the shed as long as it was well away from the house. Open the windows and if there is not much breeze put a fan in the window. It might be possible to add a few vents at or near the bottom of the shed might help also.

Don't like having gas anywhere near the house so i would keep that in the shed also. If you install an air compressor out there make sure that you are using higher quality gas cans. Some of the cheaper ones i have seen always reek of gasoline. I would not want to have a compressor sucking up gasoline fumes and packing it into a tank full of air, unless you are Blast.