Previous studies of the sizes and central densities of simulated massive, star-forming galaxies have shown that, without AGN feedback, they become too compact relative to observed galaxies at 𝑧 2. In this paper, we perform high-resolution re-simulations of a massive (𝑀 ★ ∼ 10 11 M ) galaxy at 𝑧 ≈ 2, drawn from the Feedback in Realistic Environments (FIRE) project. In the fiducial simulation, which does not include AGN feedback, the galaxy experiences a rapid starburst and shrinking of its half-mass radius at 𝑧 ≈ 2.3. In this paper, we experiment with driving mechanical AGN winds at specified, constant rates, using a state-of-the-art hyper-Lagrangian refinement technique to increase particle resolution. These winds reduce the gas surface density in the inner regions of the galaxy, suppressing the very compact starburst and maintaining a half-mass radius that is approximately constant with time. We run radiative transfer calculations to study the observable impact of AGN feedback on multi-wavelength continuum emission and find notable differences between the simulations with and without winds, in both the magnitude and spatial extent of observable short and long-wavelength flux. When AGN winds are included, the suppression of the compact, dusty starburst results in lowered flux at FIR wavelengths (due to decreased star formation) but increased flux at optical-to-near-IR wavelengths (due to decreased dust attenuation, in spite of the lowered star formation rate), relative to the case without AGN winds. The FIR half-light radius decreases from ∼ 1 kpc to ∼ 0.1 kpc in < 40 Myr when AGN winds are not included, but increases to ∼ 2 kpc when they are. The impact of AGN-driven winds at shorter wavelengths is less intuitive, with half-light radii of optical-NIR emission remaining approximately constant over 𝑡 = 35 Myr, for simulations with and without AGN winds. In the case without winds, this occurs despite the rapid compaction, and is due to heavy dust obscuration in the inner regions of the galaxy. This work highlights the importance of forward-modelling when comparing simulated and observed galaxy populations.