I'm an agency. On a not-yet-started booking, the person who paid wants to cancel within the cancellation window. We told the other guest he'd need to pay if he still wants to stay, and he agreed. But if we charge him the current price instead of the original booking price, is that a problem?

Yes, charging the current price would be a problem. If the remaining guest is made to pay more than the original booking price merely because the person who paid wants to cancel, a court or consumer arbitration committee may well treat this as an unfair commercial term.