Your module could intercept the value of "`Default 403 (access denied) page`" which is modified by the page "`Administer > Site configuration > Error reporting`":

 1. In `hook_enable`, using `variable_get`/`variable_set`, **copy the existing value** to a secondary variable and **replace the variable by your own** path (which you registered using `hook_menu`).

 2. **alter the "Error reporting" form** using `hook_form_FORM_ID_alter` to read from/write to the secondary variable

 3. If you want to be completely invisible to the user, your page callback to could call `drupal_goto( the_value_of_the_secondary_variable )`.

 4. In `hook_disable`, **restore the value** from the secondary variable.


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And that's it, your module gets notified **in a clean way** (and invisible to the user) when "Access denied" is triggered.