  Black hole solutions in general relativity come with pathologies such as
singularity and mass inflation instability, which are believed to be cured by a
yet-to-be-found quantum theory of gravity. Without such consistent description,
one may model theory-agnostic phenomenological black holes that bypass the
aforesaid issues. These so-called regular black holes are extensively studied
in the literature using parameterized modifications over the black hole
solutions of general relativity. However, since there exist several ways to
model such black holes, it is important to study the consistency and viability
of these solutions from both theoretical and observational perspectives. In
this work, we consider a recently proposed model of regularized stable rotating
black holes having two extra parameters in addition to the mass and spin of a
Kerr solution. We start by computing their quasi-normal modes under scalar
perturbation and investigate the impact of those additional parameters on black
hole stability. In the second part, we study the shadow structures of these
regularized black holes and obtain stringent bounds on the parameter space
requiring consistency with Event Horizon Telescope observations of $M87^*$ and
$Sgr\, A^*$ shadows.
