My understanding is that the "testimony" would be in the text of the password: compelling someone to reveal the password could be self-incriminating if _the password itself_ led them to additional evidence (e.g. a password of "I hid the revolver in the Conservatory"). [1]
I can't think of a case involving a fingerprint where there's a similar risk since the fingerprint is arbitrary data.
[1] https://en.wikipedia.org/wiki/United_States_v._Hubbell#Summa...