Existing methods for segmenting Neural Radiance Fields (NeRFs) are often optimization-based, requiring slow per-scene training that sacrifices the zero-shot capabilities of 2D foundation models. We introduce DivAS (Depth-interactive Voxel Aggregation Segmentation), an optimization-free, fully interactive framework that addresses these limitations. Our method operates via a fast GUI-based workflow where 2D SAM masks, generated from user point prompts, are refined using NeRF-derived depth priors to improve geometric accuracy and foreground-background separation. The core of our contribution is a custom CUDA kernel that aggregates these refined multi-view masks into a unified 3D voxel grid in under 200ms, enabling real-time visual feedback. This optimization-free design eliminates the need for per-scene training. Experiments on Mip-NeRF 360° and LLFF show that DivAS achieves segmentation quality comparable to optimization-based methods, while being 2-2.5x faster end-to-end, and up to an order of magnitude faster when excluding user prompting time.