In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decay-less, a yet unsolved phenomenon. Recent numerical work has shown that Kelvin-Helmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.