Any bike can be cabled externally. Run the housings external. Use duct tape or electrical tape to keep it in place. (Some of the new tapes hold up very well in sunlight and weather.) Might require some thought on how to provide the stops but it can be done. Not saying it will be pretty but with enough thought and a little skill, you can come close.
Modifying bikes to better serve their owners is a concept as old as the hills. We have fellows over in C & V who have done stuff to hundreds of steel bikes. Epoxies and the like open the doors to doing all sorts of stuff with CF bikes for anyone willing to do it. (And, yes, there are CF bikes where caution should be used. Same as with steel and any other material.)
I'm fully aware this is heresy to some. My view? They are just bikes. Tools/toys meant to be used.
My bikes? Well one of my best bikes, a ti custom has been cut and welded when an interference showed up after months of use. New WB bosses on I think 3 bikes. (Losing track.) A pump peg. For cabling - I always bypass the stops for rear brake bare wire along the top tube and run full length housing. So far, all my bike that have some with stops for bare wire have been steel so the 1" clamps work but if I had the same on an oversize TT, I'd have to get artistic or take it to a pro.
I wish I could remember the ingenious modifications I've done to bikes in the past. I've done a couple of fun epoxy projects. (A CF wrap around soon to break chainstays on a Peugeot that turned it into the stiffest BB'd Peugeot probably ever and came out looking near professional. But that was a save-the-frame-from -the-dumpster, not a modification.)