Yeah.... When you have a mixture of evaluating and non-evaluating cells selected, the behavior of the Cell > CellProperties > Evaluatable menu isn't obvious. I think the two states the OP wants to toggle between are:

• set Evaluatable to False for the currently selected cells, or
• reset the Evaluatable setting back to the default for those cells.

That's trivial to do with the option inspector, but it's just as easy to generate a palette to do this:

CreatePalette[Column[{
  Button["Turn off Evaluatable for Selected Cells",
    CurrentValue[SelectedCells[InputNotebook[]], Evaluatable] = False],
  Button["Reset Evaluatable for Selected Cells",
    CurrentValue[SelectedCells[InputNotebook[]], Evaluatable] = Inherited]}]]

This palette can even be installed with the Install Palette item at the bottom of the Palettes menu. Then it'll always be there in menus when needed.

For my favorite non-definitions, I will recommend (see the final lines, though best to wait until the end):

https://etc.usf.edu/lit2go/154/casey-at-the-bat/2726/casey-at-the-bat/

https://www.ssec.wisc.edu/~scottl/poem3.html

Sorry for the incomprehensible anglicism: "no joy" just means I don't get what I want. When I use the suggested keystroke, holding down the "control" key when I select a single cell, I do see a pop-up menu with Properties, but if I have multiple cells selected (which was the point of the OP) it doesn't have the options to do with Cell Properties or Evaluatable. If I have only a single cell selected and use "control" then the pop-up menu has a Properties option, but if I click on another cell (while holding down "control") that option disappears. I was trying to say that I tried holding down other keys instead, in case a Mac is different, like the "option" key and the "command" key but then I don't get any pop-up menu at all.

You said "command" works for you, so I played with some different combinations of "command" and "control" etc but I haven't been able to select multiple cells and still see the Properties and/or Evaluatable option.

On a Mac, Command works for me. What do you mean by "no joy"? Do you still get a popup menu?

Use structured selection to target all the Cells that need to have Evaluatable deactivated. To make a collection of individually targeted Cells hold down the Ctrl key while clicking. To select all Cells of the same type, hold down Alt then click on an exemplar Cell Type and all of the other Cells of the same Type will be included.

Then follow the Menu commands: Cell > Cell Properties, v Evaluatable. It will work the same way to reverse or activate them again.