I wish to use US currency ($1 bills specifically) because I want to lean on the counterfeiting security and laws. I wouldn't know how to verify paper rubles, pesos or rupees, or how unique each bill is. It would take huge balls for someone to knowingly counterfeit a FRN and send it through the US mail system.
I'm not disagreeing with your decision and reasoning but should point out that counterfeit FRNs were for sale on that tor market that was shut down and shipped via US mail.
But yes, a neat way to piggyback off the anti-counterfeit features that an ordinary person accepting the note can use to help verify its authenticity.
The USD$1 has anti-counterfeiting features? Such as?
Its main/only meaningful anti-counterfeiting feature is the one which you are voiding, its low value.
It has no security features beyond starch-free paper and even its micro-printing is not beyond the reach of cheap printers today.
Most anything else would be a better choice if you are looking for counterfeiting security, and the counterfeiting security laws will apply to any nation's currency.
If you are smitten with the USA bills, and want the advantage of the honest mistake of your customers accidentally spending it and losing the ability to redeem it, you might consider moving up to the new US$5 which have UV sensitive thread and watermarking.