Fingerprint readers are notoriously unreliable. They can have up to a 30% equal error rate (EER) that includes both false rejects and false acceptances. This can mostly be attributed to dirty fingers and/or a dirty platen / scratched platen; or a change in the fingerprint due to injury, finger cut, or change in the fingerprint pattern.
The federal government does not use fingerprint readers for biometric identification at high security facilities - they use hand geometry readers as the EER for the hand geometry reader is nearly identical to an eye retina scan at 0.00004% EER - about one false acceptance or reject in 27,000 attempts.
Much better than a fingerprint reader is a finger vein reader that uses the blood vessel pattern. However, they require a relatively high powered infrared LED to penetrate the skin surface - not applicable to something being run by batteries on a gun.
Any time I see a fingerprint reader as part of a system, I automatically reject the idea as the person making the suggestion has very obviously no working knowledge of the technology and is merely using it because it sounds good to them - and most definitely NOT because it's reliable and robust.