It depends. If the "rogue" is reversion, it shares the root system of the rest of the 'Cosmo,' and Glysophate will likely kill the whole thing.

If it's a re-seeded volunteer, the plan may work...but it also may not.

My hunch is reversion. You aren't in a good climate for the natural germination of Miscanthus seed. For that matter, your 'Cosmo' may not even produce viable seed (I grew Miscanthus spp. in Chagrin Falls, and had zero self-seeding.). Where I am now, I pull and compost hundreds of Miscanthus volunteers each year.

I'd cut off the offending blades at the crown, as soon as you detect them. I didn't even notice the all-green blades until "A" brought it up.

When you do a drift/mass/screen of a single cultivar (grass or otherwise) it's wise to have spares growing in a nursery section of the garden, to use as substitutes. DAMHIKT!

As previously suggested, you may be able to divide out the reverted section of your grass. Grow the divisions on in an innocuous section of the garden, and see what you get. Who knows, your reversions may end up as a nice wide-bladed green cultivar!?