I think the San Damiano cross is of Latin origin, more specifically was originally in the hands of Francis of Assisi. However, I think I read that it was made around the 12th Century, which would put it after the traditional schism date (1054), but well before the Schism was finalized in 1204. So I think it would be totally Orthodox.
Anyway, I'd say it's okay. Our church has one hanging in the bookstore (not for sale though), and I wore one through high school up until I was baptized and begun wearing my baptismal cross. The San Damiano cross is beautiful and I don't think ther is anything actually unOrthodox about it.