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Thanks to the release of the extraordinary EHT image of shadow attributed tothe M87* supermassive black hole (SMBH), we have a novel window to assess thevalidity of fundamental physics in the strong-field regime. Motivated by this,we consider Johannsen \& Psaltis metric parameterized by mass, spin, and anadditional dimensionless hair parameter $\epsilon$. This parametric frameworkin the high rotation regimes provides a well-behaved bed to the strong-gravitytest of the no-hair theorem (NHT) using the EHT data. Incorporating the$\epsilon$ into the standard Kerr spacetime enrich it in the sense that,depending on setting the positive and negative values for that, we deal withalternative compact objects: deformed Kerr naked singularity and Kerr BHsolutions, respectively. Shadows associated with these two possible solutionsindicate that the deformation parameter $\epsilon$ affects the geometry shapeof standard shadow such that it becomes more oblate and prolate with$\epsilon<0$ and $\epsilon>0$, respectively. By scanning the window associatedwith three shadow observables oblateness, deviation from circularity, andshadow diameter, we perform a numerical analysis within the range$a_*=0.9\mp0.1$ of the dimensionless rotation parameter, to find theconstraints on the hair parameter $\epsilon$ in both possible solutions. Forboth possible signs of $\epsilon$, we extract a variety of upper bounds thatare in interplay with $a_*$. Although by approaching the rotation parameters tothe extreme limit, the allowable range of both hair parameters becomesnarrower, the hairy Kerr BH solution is a more promising candidate to play therole of the alternative compact object instead of the standard Kerr BH. Thelack of tension between hairy Kerr BH with the current observation of the EHTshadow of the M87* SMBH carries this message that there is the possibility ofNHT violation.

No-Hair Theorem in the Wake of Event Horizon Telescope