Every pet owner has their own preferred method of walking/transporting their pet - leashes, carriers, backpacks, strollers, pneumatic tubes (just kidding, but honestly that's next). All of that's fine. I'll walk or transport their pet however the client wants.
BUT! And this is a big but, metaphorically - not my own; I will not use a retractable leash. A retractable leash is an accident waiting to happen. In fact I'm pretty sure that's on the label. "Walk your dog with the new Accident Waiting to Happen!"
If your dog gets too far ahead, the car backing out of the driveway won't see Fido. Sure you can push the button to stop the pup. But now the retractable has become a medieval garrote and folks will be wondering what kind of mob ties the dog had or if the mailman had finally had enough!
Not only that, the handle can easily slip away from you, hit the ground and clickety-clack against the pavement and scare the dog into taking off like Usain Bolt. And suddenly you're wondering what your next job is going to be because the client is gone tell 'erbody you lost their dog. And ain't nobody gonna hire the Dog Loser!
That's why I always keep a spare non-retractable leash in my bag. And when I gently inform the client that I will not be using their retractable leash, I make it clear that it's about safety. Am I a leash snob? Perhaps. But most professional pet sitters who have been in this game a while, won't use retractable leashes either.
A little snobbery goes a long way. The client will be happy and they will still have their dog intact after I walk them...unless they've already been neutered [enter rim shot here].