about coup de grace.
In PF2 there is no coup de grace. Unless you are allowing the PCs to use something like the executioner NPC's 3 action ability "behead". I know plenty of tables that do because most monsters are dead at 0hp, and important creatures get dying. Behead isn't mechanically different then using three rounds to attack. Just changes the description of events. If the target has dying 1 and takes 3 rounds of attacks they are now at dying 4 and dead anyway. Behead allows you to take an unconscious or restrained creature to dying 4 by expending 3 actions on an attack.

To answer your question.
You can draw the pistol as an action and fire the pistol as another option. Quick draw allows you to draw and use your weapon as the same action.

Interactions of holding a pistol and great sword.
You can fire the pistol while holding your sword. You just won't be able to reload the pistol without a free hand, and you won't be able to use a 2 handed sword with the pistol out.

In directions if you decide to use a two-handed firearm.
If you decided you wanted a 2 handed gun like a Blunderbuss you would either have to drop the melee weapon on the ground. (Which would require an action to retrieve if still in combat) Or spend an action putting it away. Before being able to use the 2 handed gun.

Combination weapons.
A combination weapon like a firebrand just helps with getting a free hand. As it takes a free hand to reload. It's still one interaction to transform it. Still a good idea if you can find one you like. They really shine if you plan to spend a few rounds in ranged combat and a few rounds in melee.

General advice.
Dex isn't usually a priority stat for barbarians (excepting certain builds.) guns use dex for the attack roll and this gun rolls low damage. You would typically be better off just attacking with your main weapon as you likely to do more damage. It's just a race to 0 for most monsters.

If you just want the description.
If you want to have the GM/yourself describe the ending of a combat as you pull your gun and end it that would be a swift action. And would be essentially the DM does the math and finds out you just killed the last creature with your sword. He says something like: "as you blade slices the _____ you swing wide using one hand. The other hand grabbing the pistol from your coat and ending the fight."

If you were at my table.
All that being said. I would allow you to take the following homebrew feat/action: ask your DM if they would allow something similar.

Killing blow;
Prerequisite: quick draw Allows you to use killing blow action

Killing blow; 1 action, flourish.
Requirements: successfully attacked with a melee weapon this round.
Effect: You can draw a firearm and attack treating this attack as one step better. (Crit fail = fail, fail=success, success=crit success)