Memory disaggregation is an emerging data center architecture that improves resource utilization and scalability. Replication is key to ensure the fault tolerance of applications, but replicating shared data in disaggregated memory is hard. We propose SWARM (Swift WAit-free Replication in disaggregated Memory), the first replication scheme for in-disaggregated-memory shared objects to provide (1) single-roundtrip reads and writes in the common case, (2) strong consistency (linearizability), and (3) strong liveness (wait-freedom). SWARM makes two independent contributions. The first is Safe-Guess, a novel wait-free replication protocol with single-roundtrip operations. The second is In-n-Out, a novel technique to provide conditional atomic update and atomic retrieval of large buffers in disaggregated memory in one roundtrip. Using SWARM, we build SWARM-KV, a low-latency, strongly consistent and highly available disaggregated key-value store. We evaluate SWARM-KV and find that it has marginal latency overhead compared to an unreplicated key-value store, and that it offers much lower latency and better availability than FUSEE, a state-of-the-art replicated disaggregated key-value store.