You know, I remember watching KMHM and thinking, “kdramas don’t really do this character type much.” By “like Shin Segi” I’m going to take it you mean dangerous, possessive, bad-boy types with a heart of gold.
Your best bet might be MARS. There’s a Taiwanese version and a Japanese version. I think the Taiwanese version is generally the more highly-regarded and well-loved of the two, but it is originally based on a Japanese manga.
You could also try The King’s Woman. This is a Chinese historical drama, but ML is definitely dangerous and possessive. He also has a similar reason for his attraction to FL.
For Korean dramas, the closest character I can think of is Wang So from Scarlet Heart Ryeo, but it looks like you’ve already watched it and weren’t such a fan.
These are really a stretch. I don’t think any are particularly similar, but it’s the best I can come up with.
A Love to Kill - ML is a K-1 fighter and bodyguard. He’s a bit of the dark, broody type, but he’s definitely not as sleek as Shin Se Gi.
City Hunter - ML is a highly-skilled fighter/hacker, who is taking revenge for his father's death. His personality is much more bright and cheerful than Shin Se Gi's, but he's kinda of the bad-boy, jerk type.
The K2 - Mostly ML seems rather dark because he’s a mercenary, but he doesn’t end up being as bad/dark as as he initially seems.
Lawless Lawyer - He’s more of a gangster sort of bad-boy (he's not actually a gangster, he was just raised by an uncle who is). Again, his personality is brighter than Shin Se Gi’s.
