  This paper introduces a new type of thin-shell wormhole constructed from a
special class of compact stellar objects rather than black holes. The
construction and concomitant investigation of the stability to linearized
radial perturbations commences with an extended version of a regular Hayward
black hole. Given the equation of state $\mathcal{P}=\omega\sigma$, $\omega
<0$, for the exotic matter on the thin shell, it is shown that whenever the
value of the Hayward parameter is below its critical value, no stable solutions
can exist. If the Hayward parameter is allowed to exceed its critical value,
stable solutions can be found for moderately sized thin shells. Not only are
the underlying structures ordinary compact objects, rather than black holes,
the results are consistent with the properties of neutron stars, as well as
other compact stellar objects.
