macOS - Safari function to prevent website appearing in history?
Since you do not wish to opt for Private browsing mode, you can choose to selective delete your browsing history. There are two approaches that you can take:


Clear only the recent browsing history instead of clearing all history. When you select Safari → Clear History... in the Menu bar, along with the option to clear all history you also get options to clear history for the last hour or for the current day.





You can select History → Show All History in the Menu bar, or press Command + y and selectively remove the websites by right clicking and selecting delete. This way, the website will no longer appear in history suggestion when someone else attempts to visit the same website.

However, unlike the former approach, this doesn't get rid of the cookies or login session of the website, but simply removes it from the recently visited list of websites. If you logged into a website that you removed from History, you'll still remain logged in.




Looking at your use-case, the latter option better suits your requirements. The website will not appear in history suggestion and your login session will persist. The only con is that you will have to repeatedly open History and manually remove the website(s).

Disclaimer: Do note that using these approaches may help in removing traces of browsing from your computer, but your employer/network administrator may still be logging data, recording your browsing activity. If such measures are in place in your company network, your browsing history may still be accessible to your employer (even if you browse in Private mode).