I don't that's the kind of gotcha you imply it is. Of course radiation is somehow involved in everything, it's what keeps matter together. We also read off the measurements with our eyeballs, and even if you used some sort of braille system, touching things boils down to EM interaction. The primary probe here is gravitational, any musings beyond that are of little value. I challenge you to even conceive an experiment where your own objection wouldn't apply.