Schinoussa is a place for doing very little: a small Chora on the hill, quiet coves reached on foot and evenings that end early. Paros is the opposite, with Naoussa's harbour bars, long beaches and ferries to almost every island. Most people who make this crossing are either moving back towards the busier centre of the Cyclades or heading for the Paros airport and the boats to Athens.
The direct connection is thin. Our route data lists Blue Star Ferries on it, the company that runs the large conventional ships through the Small Cyclades, and also names Small Cyclades Lines. The Small Cyclades Lines boat, the Express Skopelitis, is the local link between the small islands and Naxos, and we could not confirm that it continues to Paros, so do not count on it for a direct trip. We have no sampled timetable and Ferryhopper does not list this pair.
In practice this means you should plan the day around whatever sails. If a direct Blue Star call appears on your date, it is the simplest option. If not, the dependable way is a two-leg trip through Naxos, which is a short hop from Paros with many boats a day in summer.
Two practical points. Leaving Schinoussa is easy, because the port is a short way below the village. Arriving on Paros, you land at Parikia, from where buses, taxis and hire cars go on to Naoussa and the beaches. If you are catching a flight or a ship to Athens afterwards, leave plenty of margin.