After lots of searching, I found something that mostly works, though it's not as seamless as what I was searching for.

I set up the following Automator workflow. First I set the workflow to receive no input in any application. The first action is "Get Contents of Clipboard". The second action in the workflow is "Run Shell Script", using `/bin/bash` as the shell and passing input as arguments with the following body (most of which was automatically populated):
````
for f in "$@"; do
  open -a /Applications/Safari.app "$f"
done
````
I named my service "Open in Safari". Save.

Then I set up a global shortcut in **System Preferences** > **Keyboard** > **Shortcuts** > **Services** > **General** > **Open in Safari**, click on (none) and add my shortcut which I set to <kbd>Ctrl</kbd>+<kbd>Shift</kbd>+<kbd>S</kbd>, though it could be anything. I'm not sure if that key combination will clash with something else or not.

So now I can just right-click on a link in Outlook, select **Copy Link**, then hit my key combination to open the link in Safari. The only other side effect is that the link also gets opened in Firefox which is set as the default browser. I'd be interested to find out how to stop this behavior.