Nah, fuck that noise.
Its like killing the Joker's minions then letting the Joker go afterwards because killing is bad. The person who did it deserves the blame, and if you intentionally get your country invaded so you can seize power you deserve a hell of a lot of blame.
The only reason he might have gotten off is because by the laws put in place when his ancestor killed a ton of people to make themselves king he was a special snowflake above the law.
Obviously Cromwell is a complete asshole as well, and arguably an even worse one (*cough* likely genocide of catholics *cough), but he was right in that you shouldn't be able to walk away from killing hundreds of thousands of people just because of who your daddy was.
It is too anachronistic to judge the figures of the 17th century by the moral standards set by 21st century comic book characters. I recommend reading more about it - King Charles and Oliver Cromwell are both much more interesting than a simple tyrant or a catholic slaying arsehole. Charles' hold was strongest in England and weakest in Ireland, yet it was Ireland that supported him and England that rose against him. Cromwell is part of Irish myth as a genocider against catholics without acknowledging the ulster massacres, or the effect of seeing scores of his dead comrades piled up by men he had set free - or even the King himself, being one such man he had supported, defeated, set free - only to have to fight him again. Charles and Cromwell were both shrewd statesmen, Cromwell was a decent albeit zealous commander, and their actions display a great deal of consideration for what is just and what will restore peace to the three kingdoms. Compare it to the 20th century balkan wars where you have royalists, antifascists, fascists, communists, republicans, nationalist separatists and nationalist irredentists of Croatia, Serbia, Bosnia e.t.c. within and Bulgaria, Albania, Greece & Italy without, but you assign all blame to Tito who is like Thanos and is a bad guy who needs avengers to slap him. It's not very accommodating of all the human details lost in catastrophe, when countryman turns sword against countryman
I don't even need to think of any other reason why you wouldn't want to execute a leader who is already under your custody. For starters, put yourself in their shoes. You are part of the army faction that is supposed to represent parliament, but the parliament faction may turn against you too, and you don't know who the Royal Navy will side with. All four regions of the British isles have just recovered from a civil war and have already been plunged into yet another state of civil war, which you lack the power to end by force. Your hope that you could resolve things with a peaceful compromise have been dashed by the revelation that the King made secret pacts with your enemies, and some of your enemies broke their oaths to keep the peace. Making a second compromise with the King is now dangerous, as they have already proven they are still capable of causing civil strife in defeat. Killing the King is dangerous, as it ends all possibility of compromise and provokes the likelihood of a third wave of civil warfare against royalist-aligned factions - which is what happened. And for some shrewd parliamentarians, it would be no doubt deeply concerning that Cromwell would execute the King with authority he doesn't have, and in doing so seize powers that cannot be peacefully revoked except by an enlightened dictator. Many revolutions against tyrants ended up with Emperors who were far worse and far more powerful than the tyrants who were overthrown, which is why the manner in which governments are overthrown or replaced is so critical. People like George Washington or Lykourgos who can hold absolute authority in military and civil government and just give it all up are rare; the Napoleons, Stalins and Cromwells who end up being far more powerful and ruthless than the monarchs preceding them tend to be the rule. Violence breeds violence, and in a long & vicious civil war, it's usually the most decisive and ruthless who end up surviving. Were it not for Cromwell's incompetent son losing the confidence of the army, who knows where the commonwealth's dictatorship would have ended