Where do they keep their money?
I think it might be through voice print, consider when Beverly was buying cloth in the market on Deneb Four. Crusher: "I'll take the entire bolt. Send it to our starship when it arrives. Charge to Doctor Crusher."
"I'll take the whole bolt,"
is the legal agreement to purchase.
"Send it to our starship when it arrives,"
is the delivery destination.
"Charge to Doctor Crusher,"
in her voice is the account information.
The same with Uhura in The Trouble With Tribbles, Uhura (before it was gifted to her) intended to purchase a tribble from the bartender. But her uniform possessed no pockets, and she wasn't carrying or wearing a purse. But again she was going to buy the tribble and she earlier stated she was on the station to do some shopping.
Just as with Beverly, (imo) Uhura would have at some point made the appropriate declarative statement, and (thru eves-dropping computers) value would have been transferred from her account to that of the bar's.