  Polymer models have been used to describe non-singular quantum black holes,
where the classical singularity is replaced by a transition from a black hole
to a white hole. In a previous letter, in the context of a uni-parametric model
with asymptotic flat exterior metric, we fixed the radius of the transition
surface through the identification of its area with the area gap of Loop
Quantum Gravity. This revealed a dependence of the polymerisation parameter on
the black hole mass, where the former increases as the latter decreases, and it
also enabled the extension of the model to Planck-scale black holes. We have
identified the existence of limiting states with masses $m \geq \sqrt{2}/4$ and
zero surface gravity, showing that Hawking evaporation asymptotically leads to
remnant black holes of Planck size. In the present paper we consider solutions
with $m < \sqrt{2}/4$, observing again the presence of a minimal radius, but
without formation of horizons. Diversely from the previous mass range, only
charged solutions are allowed in this case.
