Many of my coworkers all worked for the same employer previously. That employer is now hiring. Knowing that my coworkers are still in contact with some current employees of that company, how can I apply with minimal risk that my coworkers will be informed that I applied? Is it appropriate to list your current employer as confidential on your resume and just list duties performed?
First off, no one is going to take you seriously if you choose to withhold your employer's name. You can choose to lie about it, but that might come back to haunt you later in the interview process.
If you're applying through a recruiter you may wish to explain the situation to them.
Also keep in mind that not just anyone gets to look at the resume's which are handed in for a position, especially in the early stages. It's later, when you're being interviewed by multiple department members, that some information might leak out.
However by that point you will have had contact with them and be able to explain the situation / ask for discretion.
Unfortunately what you have to understand is that there can be no guaranteed of this information not leaking out. All it takes is for one person who is friends with one of your coworkers to pick up the phone and informally laugh it up with their buddy that you're coming to work for them.
You're taking a minor risk, and that's pretty much the long and short of it.
You don't mention your industry. In software development, I would expect HR and some managers would handle the process and your current coworkers would almost certainly be unaware of what was happening. But I know in the restaurant business, people do get calls like "hey, guess what? Person A who works with you applied to work here. What are they like? Would you recommend them?" However generally such people don't then go to their boss and say "looks like Person A is thinking of moving on, I heard they applied to my old place." People are more mobile, they move from job to job, and networking serves a lot of functions. That tends to be offset by people granting you more privacy.
Your only safe thing to do is to arrange a quick chat with the relevant coworkers and ask for their help. Ask them not to tell your current management, saying that you would rather deal with that yourself once you have a new job. Also ask them to put in a good word for you with their former employer. They are likely to be flattered by this request, increasing the chances they'll agree.
Yes, there's a chance they'll run straight to your current boss and tattle on you. But you're leaving anyway, so the impact of this will not really be huge. I think it's a risk worth taking.
Why are you worried that your current coworkers will find out?
Anyway your application is not widely distributed and also only distributed to HR and people doing the hiring. They are obliged not to pass on applications as that may give you are unfair advantage/disadvantage.
So in summary just apply to the role as if it was any other role that you would apply for. I think you are over thinking the situation.