Hi,
You should be able to easily add an onchange to a characteristic or a onclick on the add to cart button.
For the characteristic dropdown, edit the file "show_block_characteristic" via the menu Display>Views and change the line:
echo $this->characteristic->displayFE($this->element, $this->params) . '</div>';
to:
echo str_replace('onchange="','onchange="callToMyCustomJavascriptFunction();',$this->characteristic->displayFE($this->element, $this->params)) . '</div>';
For the add to cart, you can edit the file "quantity" of the view "product" and change the line:
$this->ajax = 'return hikashopModifyQuantity(\''.$this->row->product_id.'\',field,1,0,\'cart\','.$module_id.')';
to:
$this->ajax = 'callToMySecondCustomJavascriptFunction();return hikashopModifyQuantity(\''.$this->row->product_id.'\',field,1,0,\'cart\','.$module_id.')';