I got lucky in that my braze-on cable guides are slotted, so with just shifting to smallest chain ring and biggest rear cog, I can manually pivot the FD out and shorten the cable (or reverse if you have a top pull FD) and on the rear, just don't pedal and shift to smallest cog. Then I can ease the housing out of the slots and gain a lot of slack. Now I can loosen the bar con shifters and re-do the wraps.
However, there is another challenge with bar con shifters and handle bar tape, and that of course, is the shifter cable run that makes two loops projecting from the inside of each lower drop on the handle bars. With STI/brifters, it's possible to just wrap the tape from bottom to top without too much interruption. But to provide an out of the cable loops, (see Brad's pic above) we require the tape be wrapped from top down to the bar end.
But RetroGrouch hints above that if the wrap is from top down, your hands, when on the tops of the drops or corners or brake hoods, will catch the edges of the next wrap and over time push them down. It's preferrable to wrap from bottoms-up for the top section of the drops. This is where brake hoods are now our friends (or enemy). If the brake hood is stretchy enough, it's possible to do the wrap in two sections and mask the discontinuity under the brake hoods and it'll still look and feel okay.
To prevent loosening, I get two-sided carpet tape and flip the brake hood up (hopefully it won't tear - but I stock extras - always) and apply some to allow the tape to stick to the lever body. The wrap will keep that stuck, but the adhesive helps prevent sliding. I also take some of the two-sided tape and tape over the bar con shifter cable housing and handle bar end. This helps keep the cable from squirming and temporarily keeps it in place. Then starting at the brake lever body, I start high and inside along the brake lever body with the tape and wrap down until I get close to the shifter, then I cut with less than 1 inch excess, stuff, push the bar con shifter into the plug, and tighten. prefer counter-clockwise for left hand, and clockwise on the right side (so the overlap seams are lined up sort of with my thumbs). (really should post some video).
For the tops, I also tape down the brake cable runs along the tops of the handlebar, then do a sort of criss-cross/over-under wrap around the tag end of the previous wrap around the brake lever body so it hides the brake lever clamp completely in the back. This provides a good anchor to then wrap from the lever up to the top. Note that there is some trial-error experience here where you should ideally spiral up the handlebar with a spiral that is "outside" leading. That means starting from the criss-cross at the brake lever body, you should exit that on the outside of the body and advance up the handlebar and wrap around the curvature relatively in a counter-clock-left, or clock-wise-right FROM the perspective of you being inside the handlebar center moving up the tubing toward the stem. What this does is slant the wrap more optimally so riding the tops and curves of the bar will increase tension on the tape making it tigher on the bars and harder to shear the adhesive and nudge the tape, as opposed to the other way which allows hand pressure to push and reduce tape tension putting all the load on the adhesive backing.
Typically, most folks use black electrical tape to secure the ends at the top. It comes in various colours too. If you're REALLY into detail, I know some folks who go all out and get heat shrink tubing, slide this onto the handlebars prior to all the wrapping, and make sure the brake cables are routed through the heat shrink, and then after the electrical tape goes on, they take a ligher and shrink down the tubing around the electrical tape to make sure it doesn't unravel. I don't go that far on my own bikes, but yes, I stock a bunch of coloured heat shrink tubing in 1 - 2 inch ID for buddies who insist. Go figure!