PhantomJs is a complete browser implementation that just doesn't render to the screen (it does have a buffer that can be captured via screenshot though). If manual testing covers the preferred browsers and you just need to know hard failures, give it a shot!
FluentAutomation.SeleniumWebDriver supports PhantomJs out of the box in current versions. Just choose PhantomJs as your 'browser' and it'll work. The FluentAutomation.PhantomJs provider is deprecated and will go away.
FluentAutomation.SeleniumWebDriver.Bootstrap(FluentAutomation.SeleniumWebDriver.Browser.PhantomJs);