The presented research on adhesives was conducted with the aim of supporting the design of composite repairs for composite aircraft structures that can withstand specific environmental conditions. Double-sided strap joint specimens of epoxy-based CFRP adherents and straps were bonded by two types of adhesives. Room-temperature curing epoxy adhesives EC-9323 and EA-9395 were used for bonding. The specimens’ shear strength and failure modes were evaluated under four different environmental conditions from −72 °C up to 70 °C unconditioned and at 70 °C after humidity conditioning. The results show that EC-9323 performed excellently at room temperature, but very poorly at elevated temperatures after hot–wet conditioning. Adhesive EA-9395 performed consistently well across all tested conditions. The failure mode analysis explained the performance trends and the effect of the environment on the fractured surface. This study will support proper repair design and verification of numerical simulations. The novelty of this article lies in its combined analysis of multiple environmental factors, providing a more realistic assessment of joint performance.