Last week I released a couple of free, open source apps named PrivateWindow and PublicWindow that will automatically open URLs in a Safari private window or non-private window. Since Apple doesn't provide any API for this, the apps use AppleScript to automatically click menu items in the Safari File menu in the main menu bar, a primitive but effective method. Or mostly effective. It turns out that this method didn't support Safari Profiles, which add items to the Safari File menu. The shortcoming has been rectified in version 2.0 of PrivateWindow and PublicWindow. The apps now let you choose which menu item to use.
Another benefit of the new feature is that you now have the ability to open URLs in a specific Safari Profile! In fact, you're not required to use the PrivateWindow app to open a new private window; instead, you could use PrivateWindow and PublicWindow to open URLs in two different Safari Profiles, such as Personal and Work. You can rename the apps in Finder to reflect your usage of them.
The latest version of PrivateWindow and PublicWindow can be downloaded from GitHub.
By the way, I'm still looking for donations of app icons to the project.