Quick answer
There is no version of this argument that ends well. Rage and laughter are both listed, and both produce the same result.
Read both lines
The verse covers the whole range on purpose. A wise man might expect that anger could at least be reasoned with and that humor might defuse things, and the saying forecloses both: וְרָגַז וְשָׂחַק וְאֵין נָחַת, he rages and he laughs and there is no rest. The word for peace is about settling, coming to rest, so what is missing is resolution rather than politeness.
This is the practical companion to 26:4–5, where answering a fool and not answering him both carry a risk. That pair said no rule exists; this verse says do not expect the conversation to conclude. Both are honest in a way that a simpler instruction would not be.
Related: Proverbs 26:4–5 · Proverbs 23:9 · Proverbs 20:3 · Proverbs 17:14
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.