Idea 1:

Blow the insides out of a normal egg, leaving the shell, and pipe in melted chocolate to fill the inside, then let cook

The issue with that approach is that the temperature at which the potential bacteria from the raw egg is rendered safe*, will ruin the chocolate. Then there's the bacteria on the outside of the shell. Many countries do not wash their eggs before sale. So it's not uncommon for the outside of the egg to have traces of faecal matter. So if you take this approach, you should heat the empty shells to a safe temperature before filling them with chocolate. Either way though, I think this method isn't a very good idea.

Idea 2:

Dip a baloon filled with cold water (or air, we have some debate about which is better) into a bath of chocolate, let the chocolate harden, then pop the baloon

This is a method that chocolatiers use but be warned that some balloons are covered in a protective powder, and there's no knowing how clean the balloon is from the factory. So it'd be advisable to clean them. Just be careful what you clean them with though, as some things such citric acid, will cause the latex of balloon weaken and pop. You can test this by putting some citrus juice on your finger and touching an inflated balloon.

The other issue is one of size. Unless you were talking about an Ostrich egg, there's a pretty significant difference in size between a chickens egg and a balloon that has been inflated enough so that it can support the weight of the chocolate without wrinkling. Filling the balloon with water will also not only make it unwieldy and much more likely to burst, it will also distort it's shape. So rather than an egg, you'll get something in the shape of a pumpkin.

The other risk you run is having the balloon pop before the chocolate is set. It might make for memorable youtube videos but cleaning the explosion of chocolate of every inch of your kitchen, including the ceiling, isn't my idea of fun... my point is, if you take this approach, just be careful to avoid creating a giant mess.

Honestly, if possible, buying a mould might be your best bet.

* Technically speaking, you could render the egg bacteria safe, whilst the chocolate is already in the egg, without ruining the chocolate. But it would take a long time and precise temperature control.