You cannot remove it entirely because the layered navigation filters need a request variable to determine what to filter. But you can change "cat" to something else.
It is defined in
public function __construct()
$this->_requestVar = 'cat';
There is a setter
setRequestVar() but unfortunately there is no way to call it between the filter being instantiated and being applied, without rewriting either the filter model or the filter block.
I would prefer to rewrite the block because the URL parameter is related to the user interface:
protected function _prepareFilter()
Since you are asking for a HACK, you could change one of the classes directly instead, but I won't recommend hacking the core. And no, copying the file to app/code/local is not better.
Now the URLs are like this:
http://example.com/redwine/dog/france. That is, the links in the filter navigation ar built this way, you could not accomplish this with
.htaccess rewrite rules.