Background: Models describing nuclear fragmentation and fragmentation-fission deliver important input for planning nuclear physics experiments and future radioactive ion beam facilities. These models are usually benchmarked against data from stable beam experiments. In the future, two-step fragmentation reactions with exotic nuclei as stepping stones are a promising tool to reach the most neutron-rich nuclei, creating a need for models to describe also these reactions. Purpose: We want to extend the presently available data on fragmentation reactions towards the light exotic region on the nuclear chart. Furthermore, we want to improve the understanding of projectile fragmentation especially for unstable isotopes. Method: We have measured projectile fragments from 10,12-18C and 10-15B isotopes colliding with a carbon target. These measurements were all performed within one experiment, which gives rise to a very consistent dataset. We compare our data to model calculations. Results: One-proton removal cross sections with different final neutron numbers (1pxn) for relativistic 10,12-18C and 10-15B isotopes impinging on a carbon target. Comparing model calculations to the data, we find that EPAX is not able to describe the data satisfactorily. Using ABRABLA07 on the other hand, we find that the average excitation energy per abraded nucleon needs to be decreased from 27 MeV to 8.1 MeV. With that decrease ABRABLA07 describes the data surprisingly well. Conclusions: Extending the available data towards light unstable nuclei with a consistent set of new data have allowed for a systematic investigation of the role of the excitation energy induced in projectile fragmentation. Most striking is the apparent mass dependence of the average excitation energy per abraded nucleon. Nevertheless, this parameter, which has been related to final-state interactions, requires further study.