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Without active galactic nucleus (AGN) feedback, simulated massive, star-forming galaxies become too compact relative to observed galaxies at z ≲ 2. In this paper, we perform high-resolution re-simulations of a massive ($M_{\star }\sim 10^{11}\, \rm {{\rm M}_{\odot }}$) galaxy at z ∼ 2.3, drawn from the Feedback in Realistic Environments (FIRE) project. In the simulation without AGN feedback, the galaxy experiences a rapid starburst and shrinking of its half-mass radius. We experiment with driving mechanical AGN winds, 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 compact starburst and maintaining an approximately constant half-mass radius. Using radiative transfer, we study the impact of AGN feedback on the magnitude and extent of the multiwavelength continuum emission. 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 to $\sim 0.1\, \rm {kpc}$ in $\lesssim 40\, \rm {Myr}$ when AGN winds are not included, but increases to $\sim 2\, \rm {kpc}$ when they are. Interestingly, the half-light radius at optical-NIR wavelengths remains approximately constant over $35\, \rm {Myr}$, 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.