Many people would say that "getting a bit worn around the edges" is a big part of leather's allure.
Shoe polish is for shoes. On a garment, it will tend to remain on the surface and transfer off to anything that touches it. It also does nothing to moisturize or condition the leather fibers.
There are colored "balms" and waxes for garment leather, but they're not all that commonly available to consumers. If you dig around, you may be able to get your hands on something like Fiebing's Atom Wax. Messy stuff.
What you'd want for (re)conditioning would be something like Apple Leather Care, Fiebing's 4-Way or Lexol. I've used all of these, and my first choice is Apple. Lexol will do, if that's all you can find, but it will darken the leather. Not a problem on a black jacket, but tan will become brown, and brown will become dark brown. I've never had a problem with Apple darkening anything, but as always, check a hidden spot first as it's always possible that formulas change.