  We give a simplified and complete proof of the convergence of the chordal
exploration process in critical FK-Ising percolation to chordal SLE$_\kappa(
\kappa-6)$ with $\kappa=16/3$. Our proof follows the classical
excursion-construction of SLE$_\kappa(\kappa-6)$ processes in the continuum and
we are thus led to introduce suitable cut-off stopping times in order to
analyse the behaviour of the driving function of the discrete system when
Dobrushin boundary condition collapses to a single point. Our proof is very
different from [KS15, KS16] as it only relies on the convergence to the chordal
SLE$_{\kappa}$ process in Dobrushin boundary condition and does not require the
introduction of a new observable. Still, it relies crucially on several
ingredients:
  a) the powerful topological framework developed in [KS17] as well as its
follow-up paper [CDCH$^+$14],
  b) the strong RSW Theorem from [CDCH16],
  c) the proof is inspired from the appendix A in [BH16].
  One important emphasis of this paper is to carefully write down some
properties which are often considered {\em folklore} in the literature but
which are only justified so far by hand-waving arguments. The main examples of
these are:
  1) the convergence of natural discrete stopping times to their continuous
analogues. (The usual hand-waving argument destroys the spatial Markov
property).
  2) the fact that the discrete spatial Markov property is preserved in the the
scaling limit. (The enemy being that $\mathbb{E}[X_n |\, Y_n]$ does not
necessarily converge to $\mathbb{E}[X|\, Y]$ when $(X_n,Y_n)\to (X,Y)$).
  We end the paper with a detailed sketch of the convergence to radial
SLE$_\kappa( \kappa-6)$ when $\kappa=16/3$ as well as the derivation of
Onsager's one-arm exponent $1/8$.
