As a starting point, on a sunny day, you are looking at f/16 at 1/125 @ISO100. 1/160s would be about f/11'7 (f/14). This would more or less properly expose the sky. To under expose the sky by 2-3 stops, you are now looking at f22'7 to f32'7. This means you would need to have a modifier/light/distance combo that can produce f/22'7 to f/32'7 to get your ratio. Once you add the ND filter, the flash and ambient will go down in ratio.
You will need that same ratio regardless of how much ND filtration you use. However, If you can increase your shutter speed (and still not exceed your x-sync speed), that will require less flash power to achieve the same goal.
One last thought is to place the area that would normally band in studio in a place that would not be noticed. Here is a link that would help explain that:
http://strobist.blogspot.com/2008/10/gr ... -sync.html