The COVID-19 pandemic has demonstrated the detrimental potential of zoonotic coronavirus transmission to human populations. Effective vaccines capable of eliciting immunity to SARS-CoV-2 have been pivotal in mitigating the spread of the virus. In this study, we describe the generation of a non-replicating pseudotyped influenza A virus (S-FLU), where the native haemagglutinin (HA) sequence is replaced with the coding sequence of either a membrane-anchored form (TM) or secretory form (Sec) of the receptor-binding domain (RBD) of the ancestral SARS-CoV-2 Wuhan (S-RBD Wuhan). We showed that both S-RBD-TM and S-RBD-Sec viruses can be generated via reverse genetics and grown to high titre. Intranasal immunisation in mice with S-RBD-TM elicits robust serum binding and neutralisation activity against SARS-CoV-2, superior to S-RBD-Sec. Furthermore, we demonstrate that a heterologous prime-boost immunisation regimen in mice with S-RBD-TM Wuhan and S-RBD-TM BM48-31 (a distant Clade 3 SARS-like betacoronavirus (sarbecovirus)) increases antibody binding breadth against mismatched sarbecoviruses compared to homologous prime-boost with S-RBD-TM Wuhan, although this did not translate into significantly enhanced cross-neutralisation across the tested virus panel. These results demonstrate that S-RBD delivery via the intranasal route induces both systemic and mucosal antibody responses and provide a foundation for further optimisation of S-RBD sarbecovirus vaccine strategies.