GQ Lup B is one of the few substellar companions with a detected cicumplanetary disk (CPD). Observations of the CPD suggest the presence of a cavity, possibly formed by an exosatellite. Using the Keck Planet Imager and Characterizer (KPIC), a high-contrast imaging suite that feeds a high-resolution spectrograph (1.9-2.5um, R~35000), we present the first dedicated radial velocity (RV) observations around a high-contrast, directly imaged substellar companion, GQLupB, to search for exosatellites. Over 11 epochs, we find a best and median RV error of 400-1000m/s, most likely limited by systematic fringing in the spectra due to transmissive optics within KPIC. With this RV precision, KPIC is sensitive to exomoons 0.6%-2.8% the mass of GQLup B (~30M_Jup_) at separations between the Roche limit and 65 R_Jup_, or the extent of the cavity inferred within the CPD detected around GQ_LupB. Using simulations of HISPEC, a high resolution infrared spectrograph planned to debut at W.M. Keck Observatory in 2026, we estimate future exomoon sensitivity to increase by over an order of magnitude, providing sensitivity to less massive satellites potentially formed within the CPD itself. Additionally, we run simulations to estimate the amount of material that different masses of satellites could clear in a CPD to create the observed cavity. We find satellite-to-planet mass ratios of q>2x10^-4^ can create observable cavities and report a maximum cavity size of ~51R_Jup_ carved from a satellite.