In this paper, we investigate spectrum sharing ultra- reliable and low- latency communications (URRLC) in an un- manned aerial vehicle (UAV)-aided cognitive radio (CR) internet of thing (IoT) network. Particularly, the secondary IoT devices opportunistically accesses the radio resource provided by a primary network and directly transmits short packets to the mobile UAV. A novel performance metric is proposed with finite block-length codes is adopted in the secondary UAV-aided IoT network. We aim to maximize the minimum average finite block-length rate for the secondary UAV-aided IoT network, subject to a probabilistic interference power constraint to the primary network based on imperfect channel state information (CSI). This formulated problem is non-convex due to the binary time scheduling, the power allocation, and the UAV altitude. In order to circumvent this issue, we develop an alternating method to solve this problem. Specifically, we first exploit the time scheduling optimization of the IoT devices for given power allocation and UAV altitude. Next, the monotonicity of the average finite block-length rate is analyzed to gain more insights for given time scheduling and UAV altitude. By capitalizing on this property, an optimal power control policy is proposed, followed by closed-form expressions and approximations for the optimal average power and the achievable average rate in the finite block- length regime. The optimal altitude of the UAV can be obtained by one-dimensional line search. Numerical results validate the effectiveness and accuracy of the derived theoretical results.