Delivery of continuous cardiopulmonary resuscitation (CPR) plays an important role in the out-of-hospital cardiac arrest (OHCA) survival rate. However, to prevent CPR artifacts being superimposed on ECG morphology data, currently available automated external defibrillators (AEDs) require pauses in CPR for accurate analysis heart rhythms. In this study, we propose a novel Convolutional Neural Network-based Encoder-Decoder (CNNED) structure with a shock advisory algorithm to improve the accuracy and reliability of shock versus non-shock decision-making without CPR pause in OHCA scenarios. Our approach employs a cascade of CNNEDs in conjunction with an AED shock advisory algorithm to process the ECG data for shock decisions. Initially, a CNNED trained on an equal number of shockable and non-shockable rhythms is used to filter the CPR-contaminated data. The resulting filtered signal is then fed into a second CNNED, which is trained on imbalanced data more tilted toward the specific rhythm being analyzed. A reliable shock versus non-shock decision is made when both classifiers from the cascade structure agree, while segments with conflicting classifications are labeled as indeterminate, indicating the need for additional segments to analyze. To evaluate our approach, we generated CPR-contaminated ECG data by combining clean ECG data with 52 CPR samples. We used clean ECG data from the CUDB, AFDB, SDDB, and VFDB databases, to which 52 CPR artifact cases were added, while a separate test set provided by the AED manufacturer Defibtech LLC was used for performance evaluation. The test set comprised 20,384 non-shockable CPR-contaminated segments from 392 subjects, as well as 3744 shockable CPR-contaminated samples from 41 subjects with coarse ventricular fibrillation (VF) and 31 subjects with rapid ventricular tachycardia (rapid VT). We observed improvements in rhythm analysis using our proposed cascading CNNED structure when compared to using a single CNNED structure. Specifically, the specificity of the proposed cascade of CNNED structure increased from 99.14% to 99.35% for normal sinus rhythm and from 96.45% to 97.22% for other non-shockable rhythms. Moreover, the sensitivity for shockable rhythm detection increased from 90.90% to 95.41% for ventricular fibrillation and from 82.26% to 87.66% for rapid ventricular tachycardia. These results meet the performance thresholds set by the American Heart Association and demonstrate the reliable and accurate analysis of heart rhythms during CPR using only ECG data without the need for CPR interruptions or a reference signal.