Would I be able to send cash from PayPal to Cash app without a record?
Lamentably, no, you can't send cash from PayPal to Cash app without a record. Thus, to make an exchange, you should have a record and furthermore add it with your PayPal account. You can likewise say that a ledger is a mediator to move cash from PayPal into a Cash app account. https://www.primotechy.com/blog/send-money-from-cash-app-to-paypal/