Not every parish can fill a group alone, and not every pastor can be away for ten days. Joining a journey another priest is already leading solves both problems: the group reaches its minimum number sooner, the smaller parish travels with a priest without having to find one, and pilgrims meet Catholics from a neighboring parish or diocese they would otherwise never have met. Nothing in the Church's life ties you to your own pastor for this. Any Catholic may attend the Mass a visiting priest celebrates, and on pilgrimage that is simply the daily Mass of the group.
The practical step is to ask the organizer two things: whether the pilgrimage is open to people outside the parish, and whether there is a deadline or a limit on numbers. Then register like any other pilgrim. If several of you are coming together, say so when you register and ask to be roomed near one another and seated together on the coach; those are ordinary requests.
Good to know before you go: when two priests travel, each brings his own celebret, the letter of introduction that shrines ask of visiting celebrants, and the organizer gives both names to the shrines when it requests Mass times. Whether a second priest's place is paid for depends on the organizer's written terms, so ask before your pastor commits. Bold Pilgrim plans its priest-accompanied pilgrimages on the same open basis.