Lightweight design of double-skin aluminium extrusions must balance structural performance and manufacturing requirements. Structural optimisation can improve mechanical performance while increasing the difficulty of extrusion, making manufacturing constraints necessary in cross-section design. For structural optimisation using continuous design variables and gradient-based search, discontinuous constraint formulations can complicate the solution process. This study formulates extrusion manufacturing requirements as continuous constraint functions of cross-section design variables and incorporates them into structural optimisation. Web–skin junction locations and member thicknesses define the section geometry. Local spacing, slot geometry and thickness relationships are calculated from this representation. The corresponding manufacturing requirements are expressed as geometric margins relative to engineering limits and updated with the design variables. Under these constraints, web layout, wall thickness and web count are jointly considered to improve structural performance. In the flat double-skin panel, optimisation reduces the web count from 14 to 10 while maintaining nearly unchanged cross-sectional area and satisfying the prescribed manufacturing constraints. Compliance under localised loading decreases by 97.80%, and flexural rigidity increases by 16.74%. Compared with a penalty-only formulation, the proposed method achieves lower feasible compliance overall with less variation across different initial sections. These results show that the continuous constraint formulation supports improved structural performance and consistent optimisation outcomes while maintaining geometric manufacturability.