Most bikes run full length outers these days. Makes for a much better sealed system. Every break in the outer is an opportunity for water and dirt ingress, so what you are describing is a great option.
As above, a compressionless outer is preferable, but I run standard Campagnolo brake cable with no problem or sponginess at the lever. Most important is to get a perfectly square cut at either end so that the cable is pulling against something solid from the start. If the outer cable is cut at an angle, the inner cable compresses inside the ferrule at either end before it pulls the brake, leading to a spongy feel.
The sticky cable guides are notoriously not very sticky, and particularly when the cable is in tension as you brake, the outer wants to snake quite a bit, so I suspect that they will be relatively easy to rip off. An alternative might be to cable tie or heat shrink the cable to as much of the gear cable as you can (assuming it isn’t a single speed?) before it needs to branch off to the other side of the frame. You can then run it underneath a neoprene chain stay protector to disguise it and keep it in place (and of course protect your stay,although obviously not from chain slap since it will be on the other side of the bike!).