The software provided with your fingerprint scanner should include a 'password safe' type feature that would allow you to login by swiping your finger. I do not have a built in one but had one years ago and the software provided with it gave me the ability to do what you suggest.

There is no way for Squenix to validate you are who you say you are via your Fingerprint scanner unless you uploaded your fingerprint to them after logging into your account manually to validate that you own the account and that is your fingerprint. With that being said I would have no desire to upload my fingerprint to every website i wished to log in to.