You need to look at so-called “shadow curing” options. Most UV-cured systems are based on acrylates and methacrylates and cure free-radically by the decomposition of a photoinitiator. However, the light or UV radiation needs to flood or be focused on the adhesive material.
It is possible build in a secondary cure mechanism to cure the areas that do not get exposed to the UV radiation. Some allylic functional monomers will crosslink by exposure to atmospheric oxygen, and it is also possible to add isocyanate functionality to generate crosslinking by atmospheric moisture, in much the same way as one-component polyurethanes do. These shadow curing systems can cure in times ranging from less than an hour to several days, depending on the system and your specific requirements.