I have a HP Elitebook and I've been trying to do the same. Doesn't seem to be a way.
Anyway, even if the password textbox is shown at login, you can still swipe the finger to login without clicking "Other Credentials" and selecting the Fingerprint icon. Fingerprint swipe works even if the password textbox is currently shown.
One thing you could do is set an impossibly long and complex password, and use the fingerprint login. But it is risky in case you forget the password and are not able to use the fingerprint swipe.
Since its HP, I would assume its an Authentec Fingerprint Reader and that you are using Truesuite Fingerprint software. Is that correct ?
You can get the full details about your hardware using Speccy
PSU: What is "PSU"?
PSU stands for Power Supply Unit