Simple assault should not have any immigration consequences for you. An employer, however, is not obligated to give you a job, and may deny your application for any reason (non-discriminatory) or for no reason at all. If the potential employer is going to do a background check it is best to level with him. That does not guarantee you a job however.
Ask your lawyer what he or she needs. Often clients fail to really communicate with their counsel. Lawyers here cannot tell you what you need to hear from your own lawyer. There is no way to tell what your employer will do with your assault. Many won't care. Others may have a different concern. Legally, your employer should only take action against you, if the conviction is relevant to the job duties, e.g. assault for security guard, DUI with delivery person driver, etc. Check with an employment attorney.
The information provided herein does not create an attorney-client relationship. The information provided is to suggerst some general principles and should not be relied upon for client decisions. Only upon the hiring of counsel can such advice be custom-tailored to the client's specific situation and needs.
I am sure your attorney who represented you for the criminal matter has advised you as to what you need to do to prepare for this interview. Aside from the letter from your attorney and your honest explanation of what occurred, there is little else you can do. Whether or not your potential employer will find this innocuous or a reason to not hire you is entirely within their discretion.