The fraction of low-mass galaxies hosting an intermediate-mass black hole (IMBH, with masses $M_{\rm BH} \approx 10^2-10^5$ M$_\odot$), is sensitive to how black hole seeds formed in the early Universe but is observationally still unconstrained. In this paper, we assemble a sample of dwarf galaxies within 10 Mpc hosting bright nuclear star clusters (NSCs) that could host IMBHs. For a subset of them, we use their observed surface brightness from {\it Hubble Space Telescope} (\hst) images, an assumed synthetic spectrum of their stellar population, Jeans Anisotropic Model (JAM) of the stellar dynamics, and the {\tt HSIM} simulator software to create mock observations with the High Angular Resolution Monolithic Optical and Near-infrared Integral (HARMONI) field spectrograph for the Extremely Large Telescope (ELT). We analyze the simulated data cube like real data, using JAM to infer the IMBH mass and its error in a Bayesian framework. Our simulations show that the ELT/HARMONI instrument can clearly detect the existence of IMBH demographics in NSCs down to a mass of about 0.5% of the NSC.