There is nothing you can spray on Creeping Charlie that will kill it and no other plant, but the soil conditions you describe are just what this "weed" much prefers so the correct solution is to correct the soil condiitons that exist, make it better so the "weed" won't grow there.
What is the level of organic matter in that soil? How well does that soil drain?

I don't know how much organic matter is in the soil but I can tell you that it's a garden that's about only 4 years old. I bought good top soil and compost and the perennials took beautifully. I leave the dead plant materials there to decompose and I rarely fertilize.

I inherited the creeping charlie from my Grandmother- I took a Hosta from her garden and I didn't realize the creeping charlie was there.

It looks great as ground cover but I am afraid it will choke off the perennials. Can they all live together and the perennials still thrive? It tangles all around my hydrangea that I also took from my grandmother a few years ago.