This study explores fully leptonic WZ and WW production at the LHC within the SMEFT framework at NLO in QCD, focusing on both CP-even and CP-odd triple-gauge-coupling dimension-six operators. We investigate the off-shell processes, contrasting our findings in inclusive setups with those in the presence of realistic fiducial selections. Alongside the conventional kinematic observables, we examine polarisation-sensitive observables and angular coefficients. Moreover, we assess potential SMEFT effects on asymmetry observables. Through a sensitivity analysis, we identify critical LHC observables that are particularly sensitive to SMEFT-induced modifications, thereby shedding light on potential avenues for new physics searches in diboson production at the LHC.