You want to display the results on a separate page, and have the sorting controls displayed but not the search filters?
So they see the results of the search but can't change the search parameters, only re-order the results?
Well, when you split the search form and the results onto separate pages, the target page will always output the search form as well as the results, it is expected in this workflow that users may want to modify their search.
You can hide the search form using CSS, but it will be added by Views to the page markup.
You can move the ordering controls out of the Filter Editor in to the items-found section of your Loop Output editor and they will still work.
I'm not sure I've understood what you are aiming to do, please elaborate if the above doesn't help.