Q: May the readings from the Common of the Dedication of a Church be used for a liturgy celebrating the establishment of the parish (not the dedication of the building) even if the actual date is unknown? If not, what readings would be appropriate?
A: That’s a good idea to turn to those readings for inspiration.
Just be aware that you’d probably be celebrating a Mass of Thanksgiving from the missal’s Masses for Various Needs and Occasions, and those readings and prayers can be used only on a day that falls below level nine on the Table of Liturgical Days. The anniversary of the church dedication, however, is a solemnity ranking at level 4b, so it’s in a different league.
If the day you’re celebrating the establishment of the parish falls within those upper levels (1-9), then you don’t have the freedom to choose readings. You use the ones assigned for that liturgical day.