You can block dates just on Airbnb and leave them open for direct bookings or other channels.

Go to Properties > Edit > Web details >> Airbnb data to the right of the property > Availability tab

At the bottom of this tab there is a button labeled Block dates.

If you have already blocked dates there will be a note to indicate how many.

Click on the button to open a calendar popup.  To block or unblock dates just click on the days.  Red days are blocked and white are available.