Replacing the current cable guide with an under-the-bottom bracket type will allow you to eliminate the current quide and also that section of cable housing that's causing you the problem. As you surmise, cable tension is sufficient to keep it in place and double-face tape is more than adequate insurance. However, it appears your rear derailleur cable is also routed above the chainstay and that will be more difficult to change as the rear cable stop will have to be replaced with an under-the-chainstay type.