Here is some code that just needs .NET with PresentationCore and WindowsBase. The underlying technology that WPF uses is WIC (Windows Imaging Component). WIC has full support for image metadata.

EXIF's ImageUniqueID is handled specifically as a Windows Property named System.Image.ImageID

Some other properties such as System.Photo.CameraModel can be seen directly in Windows Explorer detailed views if you add the corresponding column "Camera Model", but not System.Image.ImageID, AFAIK.

// needs PresentationCore & WindowsBase references
var frame = BitmapDecoder.Create(new Uri("test1.jpg", UriKind.RelativeOrAbsolute), BitmapCreateOptions.PreservePixelFormat, BitmapCacheOption.None).Frames[0];

// create encoder, add frame, we need to copy since we want to update metadata
var encoder = BitmapEncoder.Create(frame.Decoder.CodecInfo.ContainerFormat);
var copy = BitmapFrame.Create(frame);

// get frame metadata
var metaData = (BitmapMetadata)copy.Metadata;

// show existing System.Image.ImageID (if any)
Console.WriteLine("ImageUniqueID: " + metaData.GetQuery("System.Image.ImageID"));

// for some reason, we can't use "System.Image.ImageID" to set the meta data
// so use the "Metadata Query Language"
metaData.SetQuery("/app1/ifd/exif/{ushort=42016}", "My Super ID");

// write file back
encoder.Frames.Add(copy);
using (var stream = File.OpenWrite("test1copy.jpg"))
{
    encoder.Save(stream);
}