Is there a commercially available tool out there that will measure the actual throat of a skewed fillet weld?  This could become necessary with a concave weld profile.

Hg

Gal Gage Makes one.

http://www.galgage.com/measuring_gauges.html

I don't know that there is a way to measure the actual throat unless you were to section the weld and perform a macroscopic examination of the cross section.

You can measure the  legs of the weld. That is why D1.1 requires the fabricator to include the leg dimension for the skewed weld.

Best regards - Al