You're making a big assumption here: "Redesigning my checkout process will confuse people who are familiar with it".
Are people familiar with your checkout process?
So familiar that they'd be lost if it changed? It's hard for me to imagine someone getting used to a checkout process for most websites.
Unless you're running Amazon, I wouldn't be surprised if people forget the steps of your checkout process 5 minutes after they use it. But I'm also making an assumption, of course, and I'd have to find some way to test it.
Will existing users be confused by the new process?
A redesign will put your existing users in the same position as anyone who comes to the website for the first time.
I assume you're not planning to make the new checkout process confusing for new users, so why should it be confusing to existing users?
Unless they're closing their eyes and clicking on things from memory alone, it might not have as much impact as you're worried it will have.