Do you have a WD drive (either new or old one)?
If so, WD have a free version of Acronis True Image that will clone to or from a WD drive. You would also need a 2.5" external disk caddy to temporarily hold the new one.
I used one similar to
this, and the WD util is
here.
But the util will only install if one of the drives is a WD, and Windows may still have to download drivers if you have changed manufacturer.