Indeed, it should be noted that the TOS shuttles were never said to have warp drive, but also never said NOT to have it, either. It's all open to conjecture and debate.
The same goes for TNG shuttles. And in both cases, the argument can be made that the plots never require the shuttles to be warp-incapable, but they sometimes do require the shuttles to be warp-capable.
Also, VOY later explicitly reveals that some of those TNG shuttles indeed were and are warp-capable. It would be rather strange for some shuttles to have warp and others not to, when all are of roughly the same size and all have roughly the same sort of engine nacelles and otherwise closely related designs.
But in theory, we could argue that warp engines are expensive, and that factories in TOS churned out thousands of generic shuttles but only equipped a select few of those with actual warp coils inside the nacelles. It's just that no Star Trek story (excluding ENT) really requires an undamaged shuttlecraft to be incapable of warp.
Timo Saloniemi