This should not be a performance/code design question.
There should not be a performance concern with using multiple files. There is nothing precluding your properties management class(es) from being able to access multiple files - in fact, they probably should. No matter how many files you have, they should each only be loaded into memory once per jvm.
You could in theory still have one static class that handles all requests for properties. It may have multiple maps inside, corresponding to the properties file organization you choose. Whether you have multiple files or one, the code that accesses properties should know nothing about that.
On that subject of organization you choose, that is about the only decision here. If you really feel that your properties do not easily break down into multiple modules, then perhaps go with one. My feeling is go with multiple, although that's just for an organization and maintenance point of view.
just my thoughts