There are a couple of possible issues. One, if the SFF power supply is not standard sized, with standard connectors, then it is not upgradeable. This means the 380 would have to be powered by the HP power supply, haha good luck with that! Second, it's unlikely a 380 will fit in a SFF computer.
A 1050 Ti is your best possible option because they come in low profile form factors and in versions which do not require a power connector. By the way, check the documentation to make sure that model outputs the standard 75W on the motherboard pci-ex x16 slot.