Getting a recommendation letter when applying for a job before finishing graduate program
Sorry, but your problem is overconstrained. If you need two references, and all your potential references are professors, well, obviously at least two of your professors will know about your application. You could ask them not to tell others, but that's about it. In case you don't get the job you'd have to rely on them being professional about it. I'd generally expect them to be, but you know your professors better than we do.

Basically, you'll have to decide what you want the most - the job or no one to know that you're interested in the job. Alternatively, see if one or two constraints can be relaxed, including the constraints you haven't mentioned explicitly. For example, would the company be interested in waiting to hire you after graduation? Can you graduate earlier than planned? The latter is done every now and then when people are leaving for postdocs, so it's not out of the question.