Prior research has shown that typical fact-checking models for stand-alone claims struggle with claims made in conversation. As a solution, fine-tuning these models on dialogue data has been proposed. However, creating separate models for each use case is impractical, and we show that fine-tuning models for dialogue results in poor performance on typical fact-checking. To overcome this challenge, we present techniques that allow us to use the same models for both dialogue and typical fact-checking. These mainly focus on retrieval adaptation and transforming conversational inputs so that they can be accurately processed by models trained on stand-alone claims. We demonstrate that a typical fact-checking model incorporating these techniques is competitive with state-of-the-art models for dialogue, while maintaining its performance on stand-alone claims.