@privacy_ Check the SearX documentation to find out if you can use URL parameters with your settings. DuckDuckGo has parameters for everything, so after you add your custom DuckDuckGo URL to your search engines, you don't need to allow cookies or any other local site data.
On desktop, I have setup that clears everything except sites I want to remember me, but this is Impossible on mobile. The closest thing i can get, is using CookieAutoDelete (AddOn) from a custom AddOn collection to clear the Cookies, but extension level Browsing Data deletion is just not it.