Evolution of London penetration depth with scattering in single crystals of K${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$

London penetration depth, $\lambda (T)$, was measured in single crystals of K${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$, $x$=0 and 0.07, down to temperatures of 50~mK, $\sim T_c\mathrm{/}50$. Isovalent substitution of Na for K significantly increases impurity scattering, with $\rho (T_c)$ rising from 0.2 to 2.2 $\mu \mathrm{\Omega }$cm, and leads to a suppression of $T_c$ from 3.5~K to 2.8~K. At the same time, a close to $T$-linear $\mathrm{\Delta }\lambda (T)$ in pure samples changes to almost $T^2$ in the substituted samples. The behavior never becomes exponential as expected for the accidental nodes, as opposed to $T^2$ dependence in superconductors with symmetry imposed line nodes. The superfluid density in the full temperature range follows a simple clean and dirty $d$-wave dependence, for pure and substituted samples, respectively. This result contradicts suggestions of multi-band scenarios with strongly different gap structure on four sheets of the Fermi surface.