You can do what you want and you seem to understand you will need to run a sub-panel at the building/shed where the air compressor is located. Your going to make some changes however to what you have now, reason I asked the questions...it would be nice to get the answers

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If you can tell us the amperage requirements of your air compressor (probably a 20 amp circuit) we can tell you if a 10/3 cable will suffice as a feeder to a small sub in the detached building to operate the air compressor and some lights and receptacles. The cable if that is what you want to use will need to be rated for wet area installation.....for example if your wanting direct burial your 10/3G needs to be UF not nm cable like romex.
If you will answer the questions we will have a better idea of what you have and can advise you on how to get a sub-panel up and running at the detached building.
One thing I can tell you is that you cannot tap the main breaker lugs with 10/3 down to a 30 amp breaker enclosure next to the main disconnect panel.
There are tap rules but you shouldn't need to utilize them.
The most common way to run a feeder to a detached building is to install a double pole breaker in your main panel and feed the detached building sub-panel its supply off that breaker.