It can feel a bit awkward to ask someone for a written contract when they just want to shake hands and call it good. However, the reality is that handshake deals can be very problematic. You absolutely want to get that contract on paper.
For one thing, a handshake can lead to confusion in the future. You could run into a misunderstanding, or you may both remember the agreement differently. Were you supposed to get that shipment by the end of this month or next month? Exactly how much were you supposed to pay?
Keep in mind that this type of conflict does not even require one person to be dishonest. You may both honestly think that you are right and that the other person is wrong. With no paperwork to prove it one way or the other, though, how do you proceed?
On top of that, no matter how much you trust someone, you do have to think about the fact that they may intentionally try to break the terms of the deal. If they think you don't remember what payment you agreed upon, they could ask you for more. Even people you have worked with in the past may try to take advantage of the situation.
At the end of the day, the biggest question is this: Why take the risk? Why not just get that contract in writing? Even if it is awkward, it is better for both parties.
Of course, disputes even arise over written contracts. If you find yourself in the middle of one, you must make sure that you understand your rights and all of the legal options you have to protect yourself.