There's a few ways to do this
Third party transactions let you run a call on the behalf of the end user so the transaction is seamless between them. They would need to authorize your API username to run calls and then provide you their PayPal email address. The downside is if you want to process cards. The end user would have to have a Payments Pro account.
The other option is a Chained Payment, where you take the payment, take your cut and then send the rest along. In this case, however, you would be the receiver of record, not the end receiver.
The last option is to simply take the payments yourself and then use Mass Pay. Again, you would be the payee of record but you could transfer the money to the recipient's PayPal account (minus a maximum $1 fee PayPal charges).