You can block dates just on Airbnb and leave them open for direct bookings or other channels.  To do this go to:

Integrations > Channel Manager > International > Airbnb

Then click on the relevant property ID

This takes you to the Airbnb settings for the chosen property.  Click the "Availability" tab.

On 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.