Always-on keyword spotting (KWS) demands on-device adaptation to cope with user- and environment-specific distribution shifts under tight latency and energy budgets. This paper proposes, for the first time, coupling weight adaptation (i.e., on-device training) with architectural adaptation, in the form of online structured channel pruning, for personalized on-device KWS. Starting from a state-of-the-art self-learning personalized KWS pipeline, we compare data-agnostic and data-aware pruning criteria applied on in-field pseudo-labelled user data. On the HeySnips and HeySnapdragon datasets, we achieve up to 9.63x model-size compression with respect to unpruned baselines at iso-task performance, measured as the accuracy at 0.5 false alarms per hour. When deploying our adaptation pipeline on a Jetson Orin Nano embedded GPU, we achieve up to 1.52x/1.57x and 1.64x/1.77x latency and energy-consumption improvements during online training/inference compared to weights-only adaptation.