Robotic inspection of radioactive areas enables operators to be removed from hazardous environments; however, planning and operating in confined, cluttered environments remain challenging. These systems must autonomously reconstruct the unknown environment and cover its surfaces, whilst estimating and avoiding collisions with objects in the environment. In this paper, we propose a new planning approach based on next-best-view that enables simultaneous exploration and exploitation of the environment by reformulating the coverage path planning problem in terms of information gain. To handle obstacle avoidance under uncertainty, we extend the vector-field-inequalities framework to explicitly account for stochastic measurements of geometric primitives in the environment via chance constraints in a constrained optimal control law. The stochastic constraints were evaluated experimentally alongside the planner on a mobile manipulator in a confined environment to inspect a pipe network. These experiments demonstrate that the system can autonomously plan and execute inspection and coverage paths to reconstruct and fully cover the simplified pipe network. Moreover, the system successfully estimated geometric primitives online and avoided collisions during motion between viewpoints.