Is the requirement that this particular property should always be the same for this group of nodes? If it must be the same, then I would recommend extracting it into a node instead, and create relationships to that node from all nodes that should be using it.
With the value in a single place, it will only require a single property change on that node and everything will be in the right state.
EDIT
Requirements are rather fuzzy, so my answer will be fuzzy as well.
If you're matching based upon relationship types, then you'll want some kind of multiplicity on the relationship and maybe specifying allowed types in the match. Such as:
MATCH (start:RNode)-[:R45|R34|R23|R12*]->(r:RNode)
WHERE start.ID = 123 (or however you're matching on your start node)
That will match on every single node from your startNode up the relationship chain until there are no more of the allowed relationships to continue traversing.
If you need a more complicated expansion, you may want to look at the APOC Procedure library's Path Expander.
After you find the right matching query, then it should just be a matter of doing the recalculation for all matched nodes.