Supermassive black holes (SMBHs) and nuclear star clusters (NSCs) co-exist in many galaxies. While the formation history of the black hole is essentially lost, NSCs preserve their evolutionary history imprinted onto their stellar populations and kinematics. Studying SMBHs and NSCs in tandem might help us to ultimately reveal the build-up of galaxy centres. In this study, we combine large-scale VLT/MUSE and high-resolution adaptive-optics-assisted VLT/SINFONI observations of the early-type galaxy FCC 47 with the goal being to assess the effect of a spatially (non-)variable initial mass function (IMF) on the determination of the mass of the putative SMBH in this galaxy. We achieve this by performing DYNAMITE Schwarzschild orbit-superposition modelling of the galaxy and its NSC. In order to properly take account of the stellar mass contribution to the galaxy potential, we create mass maps using a varying stellar mass-to-light ratio derived from single stellar population models with fixed and with spatially varying IMFs. Using the two mass maps, we estimate black hole masses of (7.1−1.1+0.8) × 107 M⊙ and (4.4−2.1+1.2) × 107 M⊙ at 3σ signifance, respectively. Compared to models with constant stellar-mass-to-light ratio, the black hole masses decrease by 15% and 48%, respectively. Therefore, a varying IMF, both in its functional form and spatially across the galaxy, has a non-negligible effect on the SMBH mass estimate. Furthermore, we find that the SMBH in FCC 47 has probably not grown over-massive compared to its very over-massive NSC.