Shlomo Manuel,
Yes it is OK to use a Paschal greeting at any time. As a matter of fact we should be saying to our Byzantine friends HAPPY NEW YEAR since tomarrow will start their new Liturgical year and is 7919 since the creation of the Earth.
As to your friend, you have a great teaching moment with him. The Bishops' group have a good book titled Eastern Catholics in the United States of America. Get it for him (it would be a great belated New Years gift), or you could give it to him for Maronite New Years which is the first weekend of November.
Fush BaShlomo,
Yuhannon