Intelligent reflecting surface (IRS) technology has found extensive application in the wireless communication domain, offering significant enhancements in communication performance by manipulating the reflection of electromagnetic waves. This research article delves into the domain of UAV-assisted wideband cognitive radio networks augmented by IRS and underpinned by sensing-based spectrum sharing techniques. We introduce UAVs as alternative solutions for both primary and secondary base stations to optimize the management of spectral resources. Our primary objective centers around the joint optimization of both the trajectories of the primary and secondary UAVs, power allocation at the secondary UAVs, reflection coefficients of intelligent reflecting surfaces, sensing time, and subcarrier allocation, all aimed at maximizing the achievable rate of secondary users. Given that the problem at hand is non-convex, we employ deep reinforcement learning algorithms for resolution. To address the challenge of mixed-action spaces, we implement a novel Dueling DQN-Twin Delayed Deep Deterministic policy gradient (DDQN-TD3) algorithm. The simulation outcomes illustrate that the methodology introduced in this paper substantially amplifies the performance of CR system when contrasted with benchmark methods. This is evident in the improved spectrum efficiency, elevated data transmission rates, and the minimization of interference with the primary network.