Nevermind answering - for anyone else looking, here's how.
Go to Utilities | Global Options | Shortcuts

At the very top of the Options window, change the Edit Shortcuts option to Plugin: CodeBrowser (this was the step I was missing - never realized you could change this).

Set the Code Browser (Toggle) shortcut to whatever you want.

The only problem with this setup is you can Toggle the Code Browser on, but it steals focus. The Toggle off won't work until you change focus back to the editing area.

Hope it helps.