If we're sticking strictly to TNG canon, that would have to be a runabout
In Federation starship classification, a runabout was the designation of a type of vessel smaller than a starship but larger than a shuttlecraft. Runabouts were equipped with limited weapons and drive systems, but offered additional living space and the ability to be configured to mission-specific cargo capacities. They had a larger operational range and better weapons capability compared to shuttles, and were capable of speeds of up to warp 5.
Shuttlecraft in general don't get a lot of screen time before DS9 made them the main ship for several seasons. I don't think any prior shuttlecraft were shown to be warp capable. The Type 15 shuttlepod was not warp capable, and no other canon shuttles in the TNG list are shown to have warp capabilities. And saying "sensor-bearing" isn't much of a limitation (all shuttles seemed to have ample sensors).
Presumably the Enterprise could carry a Class C shuttlecraft (from ST:Discovery), which would be the fastest canon shuttlecraft-sized craft available to the TNG era (max warp 7). The Delta Flyer was after TNG canon.