This paper addresses issues of modeling Karelian-Russian code-switching for automatic speech recognition, with a focus on intra-word code-switching. Due to grammatical differences between Karelian and Russian, and the lack of automatic translation tools for languages in question, standard augmentation methods relying on parallel translated text corpora are difficult to apply. To address these issues, we developed a set of rules specifically designed for generating words with intra-word code-switching, and then augmented the Karelian text by substituting random words with their corresponding generated counterparts. Besides that, we performed linear interpolation of the Karelian language model with the Russian one. We fine-tuned Wav2Vec2.0-large-uralic-voxpopuli-v2 on both Karelian and Russian speech data with the further integration of the developed language model into the system. An evaluation demonstrates significant accuracy improvement: compared to the baseline system without a language model, we achieved relative WER reductions of 11.3% on the development set and 16.6% on the test set.