  In recent years, high-resolution transmission spectroscopy in the
near-infrared has led to detections of prominent molecules in several giant
exoplanets on close-in orbits. This approach has traditionally relied on the
large Doppler shifts of the planetary spectral lines induced by the high
velocities of the close-in planets, which were considered necessary for
separating them from the quasi-static stellar and telluric lines. In this work
we demonstrate the feasibility of high-resolution transmission spectroscopy for
chemical detections in atmospheres of temperate low-mass exoplanets around M
dwarfs with low radial velocity variation during transit. We pursue this goal
using model injection and recovery tests with H- and K- band high-resolution
spectroscopy of the temperate sub-Neptune TOI-732 c, observed using the IGRINS
spectrograph on Gemini-S. We show that planetary signals in transit may be
recovered when the change in the planet's radial velocity is very small, down
to sub-pixel velocities. This is possible due to the presence of the planetary
signal in only a subset of the observed spectra. A sufficient number of
out-of-transit spectra can create enough contrast between the planet signal and
telluric/stellar contaminants that the planet signal does not constitute a
principal component of the time-series spectra and can therefore be isolated
using PCA-based detrending without relying on a significant Doppler shift. We
additionally explore novel metrics for finding such signals, and investigate
trends in their detectability. Our work extends the scope of high-resolution
transmission spectroscopy and creates a pathway towards the characterisation of
habitable sub-Neptune worlds with ground-based facilities.
