Have tried getting WebDriver to ignore the Alert?
This can be done the following way:
var options = new InternetExplorerOptions();
options.UnexpectedAlertBehavior = OpenQA.Selenium.IE.InternetExplorerUnexpectedAlertBehavior.Ignore;
You then start WebDriver like this:
driver = new InternetExplorerDriver(options);
This is how I would do it for IE. I'm not testing Chrome but I should imagine there is a similar method for Chrome.