  We study 1/2-BPS Wilson loop operators in maximally supersymmetric Yang-Mills
theory on $d$-dimensional spheres. Their vacuum expectation values can be
computed at large $N$ through supersymmetric localisation. The holographic
duals are given by back-reacted spherical D-branes. For $d\neq 4$, the
resulting theories are non-conformal and correspondingly, the dual geometries
do not possess an asymptotic AdS region. The main aim of this work is to
compute the holographic Wilson loops by evaluating the partition function of a
probe fundamental string and M2-brane in the dual geometry, focusing on the
next-to-leading order. Along the way, we highlight a variety of issues related
to the presence of a non-constant dilaton. In particular, the structure of the
divergences of the one-loop partition functions takes a non-universal form in
contrast to examples available in the literature. We devise a general framework
to treat the divergences, successfully match the sub-leading scaling with
$\lambda$ and $N$, and provide a first step towards obtaining the numerical
prefactor.
