The recent advent of cross-lingual embeddings, such as multilingual BERT (mBERT), provides a strong baseline for zero-shot crosslingual transfer. There also exists increasing research attention to reduce the alignment discrepancy of cross-lingual embeddings between source and target languages, via generating code-switched sentences by substituting randomly selected words in the source languages with their counterparts of the target languages. Although these approaches improve the performance, naïvely code-switched sentences can have inherent limitations. In this paper, we propose SCOPA, a novel technique to improve the performance of zero-shot cross-lingual transfer. Instead of using the embeddings of codeswitched sentences directly, SCOPA mixes them softly with the embeddings of original sentences. In addition, SCOPA utilizes an additional pairwise alignment objective, which aligns the vector differences of word pairs instead of word-level embeddings, in order to transfer contextualized information between different languages while preserving language-specific information. Experiments on the PAWS-X and MLDoc dataset show the effectiveness of SCOPA.