Unmanned aerial vehicles (UAVs) have been a frontier of communication technology research for their unique advantages. Their mobility and flexibility enable their use in next-generation wireless networks. This letter explores tethered UAV-assisted hybrid cooperative communication to improve the end-to-end performance of the links between base stations and user equipment. We propose a simple, novel, channel state information (CSI)-free UAV selection policy and a hybrid PHY layer (RF or mmWave or FSO) link switching policy. We develop an insightful outage probability analysis of the proposed policy. The policy and its analysis serve as a useful analytical benchmark for UAV-assisted wireless systems.