Scratch that.
Go to PowerPress >> Settings, Advanced Mode >> Basic Settings. Make sure "Display Player and Links Options" and "No Player Option (Disable media player on a per episode basis)" are checked. Save the changes. In your individual posts, you should now see a "do not display player" checkbox within the Podcast Episode box. Check that box and when you publish the post, you should see only the PowerPress links and not the PowerPress player wherever you insert the shortcode.