The best way I found to solve this is using directly the provided View Resolver for both cases. I simply created a view (in my case a .jsp file) for "not found" responses and:
response.setStatus(HttpServletResponse.SC_NOT_FOUND);
return "error/" + HttpServletResponse.SC_NOT_FOUND;
Extra: as there can be different ways to trigger a HTTP error response, I also mapped the error pages in web.xml to have a similar view for same HTTP error code responses.
<error-page>
<error-code>404</error-code>
<location>/WEB-INF/views/error/404.jsp</location>
</error-page>
A little work for what I needed, but it made me set HTTP error handling more accurately in my application.