I can give an untested idea based on index/client/38, should be easy to modify it to work with your situation. This doesn't mean its the best way to go, just a suggestion.
In bootstrap you could do something like:
Code:
$router = $controller->getRouter();
$router->addRoute(
'client',
new Zend_Controller_Router_Route('client/:id', array(
'controller' => 'index',
'action' => 'client'));
$controller is the handle to your front controller instance eg: $controller = Zend_Controller_Front::getInstance();
That should change
http://url/index/client/38 to just
http://url/client/38. 38 being an id.
You can check the manual further, that specific routing concept is under Zend_Controller, section 7.5.2.