Multiscale and multifractal (MF) analyses have been proven an effective tool for the characterisation of heartbeat dynamics in physiological and pathological conditions. However, pre-processing methods for the unevenly sampled heartbeat interval series are known to affect the estimation of MF properties. In this study, we employ a recently proposed method based on wavelet p-leaders MF spectra to estimate MF properties from cardiovascular variability series, which are also pre-processed through an inhomogeneous point-process modelling. Particularly, we exploit a non-Gaussian multiscale expansion to study changes in heartbeat dynamics as a response to a sympathetic elicitation given by the cold-pressor test. By comparing MF estimates from raw heartbeat series and the point-process model, results suggest that the proposed modelling provides features statistically discerning between stress and resting condition at different time scales. These findings contribute to a comprehensive characterization of autonomic nervous system activity on cardiovascular control during cold-pressor elicitation.