Ensuring the effectiveness of search queries while protecting user privacy remains an open issue. When an Information Retrieval System (IRS) does not protect the privacy of its users, sensitive information may be disclosed through the queries sent to the system. Recent improvements, especially in NLP, have shown the potential of using Differential Privacy to obfuscate texts while maintaining satisfactory effectiveness. However, such approaches may protect the user's privacy only from a theoretical perspective while, in practice, the real user's information need can still be inferred if perturbed terms are too semantically similar to the original ones. We overcome such limitations by proposing Word Blending Boxes, a novel differentially private mechanism for query obfuscation, which protects the words in the user queries by employing safe boxes. To measure the overall effectiveness of the proposed WBB mechanism, we measure the privacy obtained by the obfuscation process, i.e., the lexical and semantic similarity between original and obfuscated queries. Moreover, we assess the effectiveness of the privatized queries in retrieving relevant documents from the IRS. Our findings indicate that WBB can be integrated effectively into existing IRSs, offering a key to the challenge of protecting user privacy from both a theoretical and a practical point of view.