In my opinion, <PERSON> is the same person he was when he lost his body the first time round.
For one, <PERSON> looked cosmetically like he did before, haunting <PERSON> dreams the way <PERSON> remembered him to look. You can gather from this that he looked the same as when he fell, when he was a human who was missing pieces of his soul.
The thin man stepped out of the cauldron, staring at <PERSON> . . . and <PERSON> stared back into the face that had haunted his nightmares for three years. Whiter than a skull, with wide, livid scarlet eyes and a nose that was flat as a snakes with slits for nostrils . . . 417
-GoF
Additionally, Ministry of Magic employees recognise him at the end of book 5, meaning he looks the same, and talks the same as before he was resurrected.
"I saw him, Mr. <PERSON>, I swear it was <PERSON>, he grabbed a woman and Disapparated!" "I know, <PERSON>, I know, I saw him too!" gibbered Fudge -OoTP
Essentially killing someone in the HP universe means destroying the body of a soul. As <PERSON> had split his soul, he would not be able to successfully/peacefully enter the afterlife like <PERSON> did once his soul had no more bodies/containers left in this world.
The fragment of soul inside it depends on its container, its enchanted body, for survival. It can’t exist without it." -DH
Killing <PERSON> after he has no more horcruxes would be the same as killing any other wizard, he could get maimed by a dagger (grey lady death), bleed out (when <PERSON> got splinched, he was losing blood and consciousness, which would lead to death), have his throat split (the original owner of the elder wand) or killed by any other methods that could hurt any regular human.
It's just worth noting that skilled wizards can heal injuries in ways we cannot imagine. Perhaps a gunshot wound could be healed by accio'ing out the bullet, blood replenishing potions, and a number of healing charms. Remember how <PERSON> essentially gave <PERSON> another hand after he cut it off with a dagger, which was painful and would have lead to him bleeding out.
Plus, you wouldn't need magic to kill, wizards are more than aware of guns, just not the science behind them. They know they can kill people, but just as muggles are ignorant of wizarding ways, wizards are ignorant of muggle ways. They don't use them because they have no need to.
While Muggles have been told that <PERSON> is carrying a gun (a kind of metal wand that Muggles use to kill each other) - POA 773