How to toggle Printing/Non Printing for graphic objects

Gentlemen, I thank you for the solutions and the effort. Your work really drives home the fact that I need to start my journey in the JavaScript world.

Aha -- Brian beat me to it. Two different approaches for you.

P.

There's a script here that can move all images to a new layer - not sure if it works for your needs

https://creativepro.com/topic/script-to-move-all-imagesgraphics-to-a-new-layer/

If it would be worth your while to create an Object Style

And select one of the images you want to set to non printing

And create a style for it

In the Attributes set it to non-printing and redefine the style

then you just have to turn off the non printing for 1 image and redefine the style to toggle it

Perhaps it can be scripted. 

var layerName = "Layer X";
var apis = app.activeDocument.allPageItems;
var i = apis.length;
while(i--) {
    if (apis[i] instanceof Rectangle && apis[i].itemLayer.name == layerName) {
        apis[i].nonprinting = true; //change true to false to undo
    }
}

EDIT: Here's a refined version that would nonprint all graphic containers, not just rectangles. 

var layerName = "Layer X";
var apis = app.activeDocument.allGraphics;
var i = apis.length;
var p;
while(i--) {
    p= apis[i].parent;
    if (p.itemLayer.name == layerName) {
        p.nonprinting = true; //change true to false to undo
    }
}

Here you go. Setting nonprinting is as much/little effort as moving the rectangles to a particular layer.

>  in a particular layer

In the script's text, replace xyz with the name of your layer.

r = app.documents[0].rectangles.everyItem().getElements();
for (i = r.length-1; i >= 0; i--) {
  if (r[i].itemLayer.name === 'xyz') {
    r[i].nonprinting = true;
  }
}