I work with leather often, and I would say just to leave it alone.
It would all start with what kind of leather the wrap is - that determines what sort of product you should be using. Car upholstery leather is not saddle leather is not garment leather. I can't even try to make a guess based on that image. What you're dealing with here is for sure not the same sort of leather involved with shoes, so you're entirely guessing if the polish/restoration formula will not negatively interact with how the leather is adhered to the cue.
You wouldn't want to have it dyed. Dyeing is really messy business, by nature bleeds extremely deep, and you could easily transfer it to the cue and your hand in use. I've sworn off dyeing and if I need colored leather, just purchase it that way. Even if you seal it, you're at the mercy of the sealer remaining intact before you wear through it with hand sweat. Depending on your process and the leather, it can harden out the leather and accelerate cracking/drying out.
Saddle soap involves mixing it with water, something you don't want getting onto the cue through penetration where the leather meets the wood. The secondary consequence that's real troublesome is that if you get the leather too supple, it's prone to stretching or forming a flap of excess material within your grip, or reducing the effectiveness of the adhesive so that it starts peeling off. If you must, just avoid the edges and use as little moisture as possible.
Tandy is the Michael's/Hobby Lobby of leather goods - quite expensive for low-medium grade materials possibly sold under generically a different name. I can't think of a specific product that would help here and I try to shop elsewhere whenever possible.