Within a business, there are a large variety of different ways communication can occur, each with their pros and cons.
Written communication is great if you need a clear and permanent record of a decision, correspondence or documentation. However, it is cumbersome because what can be done in a 10 minute conversation can take hours of written communication.
Unless your boss is not very busy, he will likely not have the time to engage in written correspondence with you on this.
What your boss would most likely accept is a single letter detailing all the points that you wish to raise, followed by a meeting to discuss the points. You can also prepare a list of talking points to take into a meeting if that will help you stay on track.
You can try to make it occur via written communication, but at some point in time they are likely to go: "Let's continue this in person."
You need to be quite realistic about this whole process. Unless you're changing role, or your responsibilities have grown, or will grow, it is highly unlikely there is much room to move.
You also have to keep in mind what the default position is. Unlike a job offer, a salary renegotiation has a different status quo. If no agreement is reached, the default position is no change to your salary. Unless you are willing to walk away from the job, you don't have a great deal of negotiating power. With a lack of negotiating power, it's unlikely that your boss will have a great deal of tolerance for a long drawn out negotiation.
If you're going to go back and fourth arguing over every point raised, your boss is probably more likely to say: "I have made my decision, that's final."