"He never requested me to keep it secret"... but he never says you can distribute it alone. Your job has been to develop the app. If you start distributing the app yourself you can have many more troubles (eg his paternity of idea, lost customers, lost sales, etc). 

In some countries, he who develops the app has the property of source code. However, he said he would hire another developer to complete the job, so I imagine he has the source code already. 

Consider that probably reading your Skype conversation and considering which rules (written or not) you both followed in the previous work, someone can see your behaviour as wrong and maybe an aim to damage him someway.

Maybe you can do a little agreement now to be sure you'll be paid at completion of the app (with changes not being part of the initial agreement). Even if you end up with a very low price, consider it is better then nothing, as you will reduce your present lost.

That's an error I did years ago: developing a custom e-commerce site without written agreement. I ended up with a working website that he didn't need anymore, since he had nothing to sell "at the moment". 2 months of work wasted.