I am not sure if there is an OOTB to hide some DIV while printing, but this can be achieved in this following manner.
On a click event of a button configure the below steps in order.
1) Hide the LIVE UI option by configuring Run Script. Define your own js method which can hide a DIV based on some attribute eg. data-test-id=UIInspectorButton. You can check the below fiddle for better understanding
2)Use the Print Action as you are using currently.
3) Refresh section.
In this way, you should be able to hide the LIVE UI while printing & it will not appear in the PDF.