Hi,
Then there is no solution with the options available.
Either you have the out of stock variants removed from the list, or you have them.
And the stock is always displayed after the selection of the variant.
That's because if you have two characteristics, you can't display the stock until you've selected both dropdowns.
To change that, then you would be left with custom coding as philippe said. In the file show_block_characteristic.php try to add the code:
$value->characteristic_value.= ' ('.$variant->product_quantity.')';
before the code:
if($variant->product_quantity != 0){
This will add the stock of one of the variants for the value in the dropdown.
So it will work fine with one characteristic, but if you have products with more than one characteristic, it will display a quantity that shouldn't be there.