Yes and very simple:
 
In Unleash, select the "Key Assignment" tab.
 
With your mouse, left click on the key you want to edit on the keyboard display to select it (in your case, the `~ key).  Once selected they key will appear on the lower panel.
 
On the lower panel you can assign two possible functions (Primary and Secondary) and see their current assignment.  Choose "Remap" from the drop-down menu and then select the key (using your mouse on the keyboard display) you want to remap it to (0 in your case).  If you want it to be a 0 as the default, set it under Primary.  The Secondary function is only possible when holding the FN key.   You'll see the key listed next to the drop-down box once selected/changed.
 
Make sure to hit the "Apply" button for it save - the key will then have a white highlight around it to indicate that it's been modified or given an assignment.  I believe this will be saved to the keyboard itself, so Unleash does not need to remain running (although, you're probably better off if you do leave it running).