variable scope for require

I have a limited JS interpreter for a mobile app, which does not allow usage of module.export. It has some custom global variables, say, customProp which are available at runtime, in the interpreter, in the app.

For my tests though I still need to require such JS files and define such variables. Is there a way to pass a mocked value to such custom variables during tests, when call them using require? A straightforward way would be just to add such variables to the global scope, but with many tests it becomes unusable and very error prone.

A typical script script.js:

customProp.customFuncCall(); // This works in the engine

A test test.js:

const { script } = require("./script"); // <- This throws an error: customProp is undefined

I see it is possible to pass a variable to a module when require it, but in that case, the module has to have
module.exports = function (passedVariable) {} which I cannot do.