If there was an alternative currency (paper money) unregulated by the Government would you use it?
It makes no sense to use paper money issued by someone. Paper money is, as a rule, the obligation of a country to redeem a paper note at its face value from you if you have problems selling it. Paper money is also provided with the material goods of this country.
Such paper money will be absolutely useless and will not be in demand. In addition, surely they will have very low protection against fakes.