I have a Dell Precision 7740 which shipped with no discrete graphics. Although the motherboard supports inserting a discrete GPU, the installation guide says that it has no GPU power cable. If I want a GPU, am I stuck with getting an eGPU?
No. Not for your model. Confirm with the Note in section 2. Without the power cable, you cannot do the upgrade.
NOTE: The above procedures are for UMA graphics card. Systems shipped with UMA GPU card do not have GPU power cable. However, for discrete models shipped with either a 128 MB or 256 MB VRAM GPU card, you need to connect the GPU power cable after installing the GPU card.