Hello
I have read your description and if you want to build an exchange, then you don't need to integrate Paypal or Stripe, Users can directly buy another coin through Fiat Currencies like USD or any other, which you want to keep.
Rest, if you want to exchange BTC with any other payment gateway, we can use Braintree for it as Paypal doesn't support directly for the exchange of BTC.
So for further discussion, please let me know your contact details or you can directly contact me at
arun@revinfotech.comThanks