Can you make a custom drop down in the details panel for a BP using c++ or blueprint?

You can use details panel customization (more detailed), to load your database (is stored in DataTable ?) use StaticLoadObject for single table or FAssetRegistryModule to load DataTables from specific folder/package. Of course you can then propagate dropdown with your data, check for example BlueprintDetailsCustomization CustomizeDetails function. You only need to change SEditableTextBox to STextBlock.