The implementation of non-classical light sources is becoming increasingly important for various quantum applications. A particularly interesting approach is to integrate such functionalities on a single chip as this could pave the way towards fully scalable quantum photonic devices. Several approaches using dielectric systems have been investigated in the past. However, it is still not understood how on-chip nanoplasmonic antennas, interacting with a single quantum emitter, affect the quantum statistics of photons reflected or transmitted in the guided mode of a waveguide. Here we investigate a quantum photonic platform consisting of an evanescently coupled nanoplasmonic cavity-emitter system and discuss the requirements for non-classical light generation. We develop an analytical model that incorporates quenching due to the nanoplasmonic cavity to predict the quantum statistics of the transmitted and reflected guided waveguide light under weak coherent pumping. The analytical predictions match numerical simulations based on a master equation approach. It is moreover shown that for resonant excitation the degree of anti-bunching in transmission is maximized for an optimal cavity modal volume $V_{c}$ and cavity-emitter distance $s$. In reflection, perfectly anti-bunched light can only be obtained for specific $(V_{c},s)$ combinations. Finally, our model also applies to dielectric cavities and as such can guide future efforts in the design and development of on-chip non-classical light sources using dielectric and nanoplasmonic cavity-emitter systems.