After a while of research, the answer is quite simple. Read into the source code and you'll see that it has a toolbar selector:
toolbarSelector: '[data-role=editor-toolbar]',
So you have to override that with a unique data-role
like so:
$("#consent").wysiwyg({ toolbarSelector: '[data-role=editor2-toolbar]'} );
Making sure to change the data-role
to match the new selector.