Change Private Method Sign with public for unit Test

I know that changing private method's sign with public ignore encapsulation principle. I know But I wonder that if the method does not effect or break other part of system, can i make the method's signature public?

For instance;

I have a method which contains switch-case block;

private Object foo(Object object, MyTypeEnum type) {
    ....
    switch(type) {
      case type.x:
         return "a";
      break;
     case type.y:
         return "b";
      break;
     case type.z:
         return "c";
      break;
     .
     .
     .
  }
  ..
 }

In addition;

• Moving the method in utils class to be able to make its sign public is bad practise since the method is not generic and reusable
• Testing a public method which calls the private method(foo) is one of solutions. However, my codebase has a lot of legacy and untested code so i have to change other classes and methods. Furthermore, I have no enough time refactor other part of my codebase.

What do you advice to me for this case ?