We present an analysis of the JWST NIRCam and MIRI morphological and structural properties of 80 massive (log10(M*[M_{sun_)])=11.2+/-0.1) dusty star-forming galaxies at z=2.7^+1.2^_-0.7_, identified as sub-millimetre galaxies (SMGs) by ALMA, that have been observed as part of the JWST PRIMER project. To compare the structure of these massive, active galaxies to more typical less actively star-forming galaxies, we define two comparison samples. The first of 850 field galaxies matched in specific star-formation rate and redshift and the second of 80 field galaxies matched in stellar mass. From visual classification of the SMGs, we identify 20+/-5% as candidate late-stage major mergers, a further 40+/-10% as potential minor mergers and 40+/-10% which have comparatively undisturbed disk-like morphologies, with no obvious massive neighbours on . 20-30kpc (projected) scales. These rates are comparable to those for the field samples and indicate that the majority of the sub-millimetre-detected galaxies are not late-stage major mergers, but have interaction rates similar to the general field population at z~2-3. Through a multi-wavelength morphological analysis, using parametric and non-parametric techniques, we establish that SMGs have comparable near-infrared, mass normalised, sizes to the less active population, R_F444W_50=2.7+/-0.2kpc versus R_F444W_50=3.1+/-0.1kpc, but exhibit lower Sersic indices, consistent with bulge-less disks: n_F444W_=1.1+/-0.1, compared to n_F444W_=1.9+/-0.1 for the less active field and n_F444W_=2.8+/-0.2 for the most massive field galaxies. The SMGs exhibit greater single-Sersic fit residuals and their morphologies are more structured at 2um relative to 4um when compared to the field galaxies. This appears to be caused by significant structured dust content in the SMGs and we find evidence for dust reddening as the origin of the morphological differences by identifying a strong correlation between the F200W-F444W pixel colour and the 870um surface brightness using high-resolution ALMA observations. We conclude that SMGs and both massive and less massive star-forming galaxies at the same epochs share a common disk-like structure, but the weaker bulge components (and potentially lower black hole masses) of the SMGs result in their gas disks being less stable. Consequently, the combination of high gas masses and instabilities triggered either secularly or by minor external perturbations results in higher levels of activity (and dust content) in SMGs compared to typical star-forming galaxies.