I work for a women's shelter and wanted to know if it was possible to make our website not appear in their browser's search history.
Despite Incognito mode and deleting your history being obvious choices, some survivors seeking help may not know about those features, especially considering some circumstances where they're actively kept in the dark about the outside world by their abuser, and abusers in-turn can use that lack of knowledge to control and monitor them.
For context, we contracted another company to design and run the site; I just work in the IT department, and they were asking everyone for suggestions.
Without user's permission you can not do anything even if you will be able to code. It has to ask each time to user to give permission for modification because your website is gonna be 3rd party and without granting permission from the user's side it is not possible. The best way is to hack and install extensions to the user's device. After installing the extension you have to add a website URL that you want not to be shown in history.
For Firefox https://addons.mozilla.org/en-US/firefox/addon/history-autodelete/
For Chrome: https://chrome.google.com/webstore/detail/history-blocker-by-site/keamekimefemnbgegbfkdkmbomaahfai?hl=en