Thin HgCdTe/CdHgTe quantum wells (QWs) grown on alternative GaAs (013) substrates have been recently proposed as a material for coherent emitters in the mid-IR region. In this work, we develop a technological process for the fabrication of ridge microresonators in waveguide heterostructures with multiple HgCdTe QWs via photolithography and ion etching. We process two samples with different ridge heights and analyze their emission spectra measured under optical excitation. The width of the emission spectra dropped by an order of magnitude compared to the nonprocessed as-grown structure, allowing one to conclude that lasing at 9.2-7.1 µm takes place within the 8-120 K temperature range. However, both samples demonstrated faster temperature quenching of lasing than that of the single-pass stimulated emission from the nonprocessed structure, as well as a drop in the carrier lifetimes. These figures of merit are likely to be compromised not by the Q factor of the cavities, but due to defects induced during the etching process. Finally, the implications for HgCdTe-based lasers for the 3-5 µm transparency window and longer wavelengths (beyond 20 µm) are discussed.