Query correction is a critical entry point in modern search pipelines, demanding high accuracy strictly within real-time latency constraints. Chain-of-Thought (CoT) reasoning improves accuracy but incurs prohibitive latency for real-time query correction. A potential solution is to output an answer before reasoning to reduce latency; however, under autoregressive decoding, the early answer is independent of subsequent reasoning, preventing the model from leveraging its reasoning capability to improve accuracy. To address this issue, we propose Sandwich Reasoning (SandwichR), a novel approach that explicitly aligns a fast initial answer with post-hoc reasoning, enabling low-latency query correction without sacrificing reasoning-aware accuracy. SandwichR follows an Answer-Reasoning-Answer paradigm, producing an initial correction, an explicit reasoning process, and a final refined correction. To align the initial answer with post-reasoning insights, we design a consistency-aware reinforcement learning (RL) strategy: a dedicated consistency reward enforces alignment between the initial and final corrections, while margin-based rejection sampling prioritizes borderline samples where reasoning drives the most impactful corrective gains. Additionally, we construct a high-quality query correction dataset, addressing the lack of specialized benchmarks for complex query correction. Experimental results demonstrate that SandwichR achieves SOTA accuracy comparable to standard CoT while delivering a 40-70% latency reduction, resolving the latency-accuracy trade-off in online search.