Switching gateways should always be done with care, but works pretty seamlessly. Some notes:
* If you leave the API information for the old gateway (PayPal in this case) populated when switching to the new gateway, those values will be stored in the background and...
* Your existing PayPal subscriptions will not be cancelled (unless people checkout again)
* If users who signed up on PayPal cancel or change membership level, their PayPal subscription will be cancelled.
So you should in theory be able to just enter the Stripe information and switch over to Stripe. Your old users will continue to be billed through PayPal until they either cancel or checkout again (at which time their PayPal subscription will be cancelled and a Stripe subscription will be created.) People will often create incentives to "upgrade" etc for users to checkout again to consolidate their billing.
Hope this helps.