I think the most common way is to create static methods. As an example see StringUtils in Apache Commons Lang, Strings in Guava or even Arrays in JDK.
Also the class should be made final and it should have a private constructor to avoid inheriting it or instantiating it.
Either you use static methods or a singleton, it should be the same effort to unit test it. In the latter case, you might write a little bit more code (characters).
I know that OO purists will argue the very existence of such classes and I will tend to agree with them, but these are added only for the sake of simplicity and you should limit the number of such classes.
