Would it make sense for that singleton to implement an interface, allowing you to mock out those methods for test purposes?
I know it goes against testing dogma these days, but in certain situations I think a static method is fine. If it's the kind of behaviour which you're never going to want to fake for test purposes, and which is never going to be polymorphic with other implementations, I don't see much point in making a singleton. (Singletons are also generally the enemy of testability, although if you only directly refer to them in the injection part of your code, they can implement appropriate interfaces so their singletoneity never becomes a problem.)
It's worth mentioning that C# has "static classes" for this kind of situation - not only do they prohibit other code from deriving from or instantiating the class, but you can't even use it as a parameter. Basically it signals the intent very clearly.
I would definitely suggest at least having a private constructor to prevent instantiation by the outside world.