Logically, one could make excuses about destroying robots, but it sort of goes against the challenge of a no kill run. Besides that, your combat skills probably wouldn't be up for it anyway.
Grace having NO weapons shows a bit of poor strategy on her part. Wounding would be necessary for several quests, and if nothing else, disarming people was an option in Fallout 3 and New Vegas. It wouldn't help against giant monster lizards, but any weapon can be shot out of enemy hands, and its condition ruined past the point of use in the process. They might still try to punch people and/or find another weapon, but it's something Grace should definitely be doing.
There aren't any robots that look like that in New Vegas, but I'm taking design liberties all over the dang place in this storyline, and I wanted to make the robot look like one I built in the Fallout 4 Automatron DLC named Coastguard. Coastguard has a special place in my heart because one, he's the most powerful robot I've made, and two, I somehow made him hostile towards me.
I had no idea whether this meant other robots I'd made would be mad at me, so between Coastguard's power and all the other robots I'd made, I was on the run from my own creations for a while. I eventually found a place to lay low for a couple in game days, giving Coastguard time to chillax. Coastguard is no longer hostile towards me, but I'm extra cautious around him now.