The intensity of tropical cyclones is highly dependent on air–sea enthalpy and momentum exchange. At extreme wind speeds, the values of the enthalpy, CK, and momentum, CD, exchange coefficients are characterized by high uncertainty. The present study aims to expand the previously used algorithm for CD retrieval to obtain the values of CK from wind speed measurements and the enthalpy profiles obtained from NOAA GPS dropsondes in hurricane conditions. This algorithm uses concepts from technical hydrodynamics, describing turbulent boundary layers on flat plates and pipes. According to this approach, the velocity (and enthalpy) defect profiles are self-similar in the entire boundary layer, including the layer of constant fluxes and the “wake” part, where the airflow adapts to the undisturbed flow region. By using the self-similarity property, the parameters of the constant flow layer (the roughness parameter, friction velocity, and the enthalpy and exchange coefficients CD and CK) could be obtained from measurements in the “wake” part for wind speeds from 20 m/s to 72 m/s. The estimates of the CK/CD ratio revealed values of 0.7 and 0.96 (depending on the self-similar approximation limits), and the results suggest that there are slight variations with the wind speed.