Stochastic cooling of the Spectrometer Ring (SRing) at the High Intensity heavy-ion Accelerator Facility (HIAF) project in China, which is used mainly for experiments with radioactive fragment beams, is applied to speed up the cooling process of a stored ion beam. In this study, both a Faltin traveling wave structure and a novel slot-ring standing wave structure based on a ceramic vacuum chamber are discussed and evaluated for the pickup/kicker of the SRing stochastic cooling system. The slot-ring structure should significantly improve the shunt impedance due to the Cherenkov effect. For the Faltin-type structure, the results for the pickup shunt impedance obtained from simulations and from beam measurements agree well. Good agreement is also found between the simulated and measured results for the pickup shunt impedance of the slot-ring structure. Cooling process simulations using the Fokker-Planck equation based on the shunt impedance results for the Faltin and slot-ring type pickups are also presented.