  Upcoming wide-field spectroscopic surveys will observe galaxies in a range of
cosmic web environments in and around galaxy clusters. In this paper, we test
and quantify how successfully we will be able to identify the environment of
individual galaxies in the vicinity of massive galaxy clusters, reaching out to
$\sim5R_{200}$ into the clusters' infall region. We focus on the WEAVE Wide
Field Cluster Survey (WWFCS), but the methods we develop can be easily
generalised to any similar spectroscopic survey. Using numerical simulations of
a large sample of massive galaxy clusters from \textsc{TheThreeHundred}
project, we produce mock observations that take into account the selection
effects and observational constraints imposed by the WWFCS. We then compare the
`true' environment of each galaxy derived from the simulations (cluster core,
filament, and neither core nor filament, {``NCF''}) with the one derived from
the observational data, where only galaxy sky positions and spectroscopic
redshifts will be available. We find that, while cluster core galaxy samples
can be built with a high level of completeness and moderate contamination, the
filament and NCF galaxy samples will be significantly contaminated and
incomplete due to projection effects exacerbated by the galaxies' peculiar
velocities. We conclude that, in the infall regions surrounding massive galaxy
clusters, associating galaxies with the correct cosmic web environment is
highly uncertain. However, with large enough spectroscopic samples like the
ones the WWFCS will provide (thousands of galaxies per cluster, {out to
$5R_{200}$}), and the correct statistical treatment that takes into account the
probabilities we provide here, we expect we will be able to extract robust and
well-quantified conclusions on the relationship between galaxy properties and
their environment.
