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Actually...

"Physical sky without sun" means that we get the color-gradient of the sky relative to the hour of the day, but we avoid casting shadows on the scene. So it is basically global illumination with an added background sky gradient.

Yes, when using "physical sky without sun" you can supplement your own custom made Sun via emitter in the distance.

What confuses me in your explanation is that the link shows an outdoors scene but your render shows an indoors situation. Are you planning to show the indoors object using physical sky ?

Studio setup is the best way to go IMHO with this scene. One thing to note is that in studio, the color of the emiters is very important. Try to use B-type emiter for the lightsource on the left. Alternatively try a D75 for the left emitter and B-type for the small ones under the counter.

I wouldn't use physical sky for objects. Others have been there, done that and the result is often kinda goofy (or at least doesn't look professional).

In your case you need to bring a back wall in the scene. Right now you object is in the middle of infinity.

Try to think in physical terms... what would there be in your surroundings if you were to build this thing and take a picture ?

You can try to create a sphere engulfing the scene and apply an emitter material with an mxi map... provided you can find a suitable background image.