I am going to agree with the others in this thread whom have claimed that killing prisoners that have surrendered after you have promised to let them go if they give you information is evil. Specifically Chaotic Evil. We literally have international laws that are designed to prevent such actions in wartimes, and that specific sort of lying and ruthlessness is exactly the sort of thing a villain would do. Hell it's a common thing for Joker in Batman who is the practical poster boy for Chaotic Evil.
That all said, there is nothing wrong with having chaotic evil characters in a party, but there should be consequences for their actions (more on that in a bit).
What mainly concerns me, however, is this:
So to start with I don't like Paladin PCs. Did not like them in 1Eor 3E, 5E is a little better but they still have that silly oath. They are great for that knucklehead NPC.
Right here is your real problem, you have a self-stated strong bias against paladins that can and will cloud your judgement on this issue, and frankly you should've told the player not to play this character if you cannot or are not willing to overcome said bias in order to make the game fun for him as well as the rest of the group.
What might be the best thing for the group collectively is for him to reroll to another character, but the issue isn't just Paladins or their oath, and I assure you it will not just "go away" if he just rolls a fighter. What you've an issue with is a miscommunication of expectations on the part of what are clashing wants/needs from the game for your different players and yourself.
OF course they were ambushed by said giant and friends later that session.
This right here is again said bias popping up. You say "of course" when I say how was this a certainty that the giant would come back? He could've gone his separate ways and decided to vent his anger and stress on another weaker target. Less specific to the giant, this is a negative instance that the rest of the group will surely use as "proof" that their evil ways are better and the paladin is dumb for being the only one in the group that values lives.
Additionally, I should hope that the rest of the groups actions have consequences that are "of course" the logical outcomes as well:
Actions and deeds get around, if a particular group of adventurers develop a reputation for not honoring their word over prisoners not only should they NEVER expect mercy or kindness on the part of their foes should they lose, but they should realistically expect others to not with to work with or hire them. After all, why would a random tavern keep want such bloodthirsty people in his inn? Why should the king trust to hire cutthroats who do not honor their word with their prisoners? What happens when they murder a noble whom they've interrogated? It's not like no one would investigate them going missing and I remind you that speak with dead is a spell.
These are the natural results of such behavior and they should expect it to happen. Hell, who's to say they shouldn't get ambushed by a group of holy paladins seeking to slay this group of "honorless murdering psychopaths" they heard are "terrorizing the countryside".
If you are going to effectively punish the paladin for roleplaying his character, you should do the same with the rest of the group. Were I the paladin player I
would reroll, and when I did I would secretly inform the DM that I would want to have the character head off directly to the church of Tyr and inform all he can about precisely ALL of the things that they have been doing, just to attempt to force said ambush to occur. Furthermore, depending on if I felt it justified, my next character would not only be
firmly Chaotic Evil just to further spread this bad reputation and outright caricature the rest of the groups actions, but I might even mentally clock out of any investment I had in the game for the rest if the campaign (and possibly longer).