  The CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ superconductors resemble the
archetypal 122-type iron-based materials but have a crystal structure with
distinctly lower symmetry. This family hosts one of the few examples of the
so-called spin-vortex crystal magnetic order, a non-collinear magnetic
configuration that preserves tetragonal symmetry, in contrast to the
orthorhombic collinear stripe-type magnetic configuration common to the
122-type systems. Thus, nematic order is completely absent from its phase
diagram. To investigate the evolution of nematic fluctuations in such a case,
we present elastoresistance and elastic modulus measurements in
CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ ($x = 0-0.05$) combined with
phenomenological modeling and density functional theory. We find clear
experimental signatures of considerable nematic fluctuations, including
softening of the Young's modulus $Y_{[110]}$ and a Curie-Weiss type divergence
of the B2g elastoresistance coefficient in
CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$. Overall, nematic fluctuations within
this series bear strong similarities to the hole-doped
Ba$_{1-x}$K$_x$Fe$_2$As$_2$ series, including a substitution-induced sign
change. Our theoretical analysis addresses the effect of the specific crystal
symmetry of the 1144-type structure in determining its magnetic ground state
and on the nematic fluctuations.
