The funny thing is that we'll probably get around to detonating some nuclear weapons, but I doubt it will be in a controlled attempt to avert catastrophe. More like it will be the final act in a series of wars over resources and migration (although who knows how it will be couched politically/popularly). When one group is up against a wall called "annihilation", they'll push the button.

We've got launch capability, and we've launched solar sails before.

Now we've got to launch either a really massive solar sail or a lot of small ones. And they've got to be really massive or have enough fuel to maintain position.

You could setup the shield around Lagrange point 1 which has the advantage of not creating noticeable rings around the earth. This does not reduce material needed by all that much, but it does prevent kessler syndrome as your sunshade breaks down.

However, a much cheaper option is simply cover large regions of the earth with a reflective coating. Between those extremes are things like hot air balloons in the upper atmosphere.

Or you know, polluting with vast quantities of SOX. You're dreaming too big, and not dirty or dumb enough.

I can't begin to imagine the difference in scale here. Perhaps a solar sail a few million times larger than all the solar sails we've ever launched, combined?