Paul, the way I personally insert sharps and flats is like this, but I don’t know whether you’ll like it! Go to Keyboard in System Preferences, choose the ‘Input Sources’ page, and add ‘Unicode Hex Input’. Switch on the ‘Show input menu in menu bar’ checkbox if it’s not on already.
Now do Shift+X to start some text in Dorico. When you want to type a sharp or a flat, switch to the ‘Music text’ character style, which you can do using the menu in the top right-hand corner of the text editing popover. Now switch to Unicode Hex Input in the input menu in your Mac’s menu bar (the menu is hiding behind an icon that looks like a little national flag, for me a British flag). Now hold Alt and type 266D for a flat, 266F for a sharp, or 266E for a natural.