I am counting on there being enough Starlink satellites to block out the Sun. Problem solved.
Feasibility of cooling the Earth with a cloud of small spacecraft near the inner Lagrange point (L1) https://www.pnas.org/content/103/46/17184
The better the efficiency of the solar panels, the worse the shadowing effect. Even worse, the solar array in orbit also reflects heat back at Earth! If the size of the array is significant enough to shadow Earth from the sun, it's obviously significant enough to impact this flipside of the balance of radiative transfer. Keeping it on the day side always would offset that ... maybe - but for that it would have to be in solar orbit.
Any energy you transfer to Earth (fusion reactors in orbit, off-planet solar arrays, whatever) is part of it, the form of energy does not matter much, almost all of it is heat in the end and affects the thermodynamic equilibrium of the planet.
As an exaggerated example, if you put a giant solar array into solar orbit and beamed the converted power to Earth, it's like Earth suddenly having a larger surface but just for receiving solar radiation. For the purposes of Earth radiating heat back into space, the solar array does nothing.
Sure, the effects wouldn't be multiplied as with an atmosphere with too many far IR-scattering molecules that we have now but the power wouldn't come for free.
Besides, whatever the power conversion technology is, it's unlikely to be anywhere near 100% efficient. That means you need to be getting rid of thermal energy in large quantities anyway. As long as you're at least pointing that away from Earth, it's a win.