You yourself said that there is "no equilibrium", but then forgot that Le Chatelier's principle only applies to any system at equilibrium! Recall its definition:
Le Chatelier's principle: a principle stating that if a constraint (such as a change in pressure, temperature, or concentration of a reactant) is applied to a system in equilibrium, the equilibrium will shift so as to tend to counteract the effect of the constraint.
In your case, as also MaxW pointed out above, $\ce{NaOH}$, $\ce{HCl}$ and $\ce{NaCl}$ are all completely ionized in water (and their ions are hydrated/solvated by water molecules). There is no such thing as an "equilibrium" in this case, as the reaction, being an ionic reaction, completely proceeds in the forward direction.