So, you want to eliminate cables that interfere with your front bag. What type of bike is this, and what is the gearset? If indexed, you could potentially switch to combination shifter/brake levers that are compatible. Or, you could run the housing up beneath the bar tape to the stem.
Or, you could swap in downtube shifters. They are the simplest.
By doing this ^ you will change a major control element of your bike. I ride downtube shifters on two of my vintage bikes, and the ergonomics are different, as are the balance requirements. Shifting is a lot more frequent action than grabbing a water bottle. On the downtube, you have to anticipate shifts a bit earlier. It's not as convenient as shifting on the bars. I find that I have to be more alert in traffic, near the "door zone", stopping at traffic signals on descents, and on incline changes mid-climb. These all require better anticipation and more physical control (by the rider) than when shifting similarly from the handlebars. Just something to consider.