You can also restrict HTTP Response Headers with the LTM HTTP Profile.
Use the "Response Headers Allowed" flied to specify a whitespace delimeted list of allowed headers. Of course you wouldn't have any logging, but it's faster.
Example:
[root@bigip:Active] config tmsh modify ltm profile http YOUR_HTTP_PROFILE response-headers-permitted add { Accept-Range Cache-Control Content-Encoding Content-Length Content-Type Etag Last-Modified Pragma Set-Cookie }
For documentation see AskF5:
https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/ltm-concepts-11-2-1/ltm_http_profiles.html