Unit Testing Dependencies

Sometimes it seems that creating a test double ("Mock", "Stub", etc) of a class makes sense. It isolates the unit that needs to be tested and filters out irrelevant noise.

However, what happens when I need a test double that has to actually do the work? In that case, how should I unit test close dependencies?

Suppose I have a class like such:

public class StringFunctions()
{
    public string CapitalizeString(string str)
    {
        // return a string of letters that all need to be capitalized.
    }
}

And I have a class that uses StringFunctions as a dependency:

public class MyStringFunctions()
{
    private StringFunctions _strFuncs;

    public MyStringFunctions(StringFunctions strFuncs)
    {
        _strFuncs = strFuncs;
    }

    public string Put3AtEndOfStringAndCapitalize(string str)
    {
        return _strFuncs + 3;
    }
}

So now I would like to Test the method Put3AtEndOfStringAndCapitalize

Based off of the spec, I would like to give the method some conditions as such and I would expect:

cat => CAT3
THING => THING3
TEST3 => TEST33

In this case, how would I unit test MyStringFunctions using a "Test Double" of StringFunctions? The issue I'm having is that the "Test Double" needs an actual working CapitalizeString method.In this case, would it be best to not do any mocking?