Daytrip from Naxos to Mykonos with greek island ferry pass

Hi, we have bought a 4 day greek Island pass. When we are planning to stay in Naxos, we want to take a daytrip to Mykonos. But the only ferries we can take from the attica group is too long between (arriving 12:10 and departure 22 something). So I was wondering if I can use the pass on the ferry to Mykonos and then we order a ferry back to Naxos with another ferry company and pay ourself. But when we are done staying in Naxos and on our way to Santorini, will this be a problem in our passes? Because it will look like we are traveling from Mykonos? Since that would be the last travel day in the passes.