  Bardeen's 1968 idea of a regular black hole spacetime was revived by Hayward
in 2006 through the construction of a new example of such a geometry. Later it
was realised by Neves and Saa, that a wider, two-parameter class exists, with
Bardeen and Hayward spacetimes as special cases. In this article, we revisit
and generalise the Hayward spacetime by applying the Damour-Solodukhin (DS)
prescription. Recalling the DS suggestion of a deformed Schwarzschild spacetime
where $g_{tt} = -\left (1-\frac{2M_1}{r}\right )$, $g_{rr} = \left
(1-\frac{2M_2}{r}\right )^{-1}$ and $M_1\neq M_2$, we propose a similar
deformation of the Hayward geometry. The $g_{tt}$ and $g_{rr}$ in the original
Hayward line element remain functionally the same, {\em albeit} mutations
introduced via differently valued metric parameters, following the DS idea.
This results in a plethora of spacetime geometries, known as well as new, and
including singular black holes, wormholes or regular black holes. We first
study the geometric features and matter content of each of such spacetimes in
some detail. Subsequently, we find the scalar quasinormal modes corresponding
to scalar wave propagation in these geometries. We investigate how the real and
imaginary parts of the quasinormal modes depend on the values and ranges of the
metric parameters used to classify the geometries. Finally, we argue how our
results on this family of spacetimes suggest their utility as black hole
mimickers.
