かなりいいと思います。もうこれで決定ですね。
あえて何も説明を書かないが、わかる人がわかると思います。

'use strict'

let Cat = (function() {
    let _share = 'only one';
    let privates = new WeakMap();
    let $ = function(o) {
        return privates.get(o);
    };
    function Cat(name) {
        privates.set(this, {});
        $(this).name = name;
    }
    Cat.prototype = {
        //self:function(){return privates.get(this);},
        init:function(){},
        load:function(){},
        say:function(){console.log('my name is', $(this).name)},
        getShare:function(){console.log(_share);},
        setShare:function(newValue){_share = newValue}
    };
    return Cat;
})();

let cat1 = new Cat('cat1');
let cat2 = new Cat('cat2');

console.log(cat1);
console.log(cat1 === cat2);
console.log(cat1.init === cat2.init);
console.log(cat1.load === cat2.load);
console.log(cat1.name);
cat1.say();
cat2.say();
cat1.getShare();
cat2.getShare();
cat1.setShare('share changed by cat1');
cat1.getShare();
cat2.getShare();

Q：継承はとうなるの？
A：継承？Javascript 継承させる？