Sorry to be the wet blanket here but experience has taught me that contracts which are not clearly defined to both parties are a disaster. The expectations and understanding of one party may well not be the same as the other and the whole thing degenerates into a "he said, she said" argument.
For example, in your "handshake" deal, did you both know the payment terms? It's very easy in Europe to expect payment in 30 days but your Middle Eastern client will pay as he does normally in 120 days leaving you with no cashflow.
The other point concerns the avoidance of corruption. Your handshake morphs into passing brown envelopes.
However, it is not necessary for lawyers to crawl over most normal business contracts.