a classic design would actually look pretty cool imo
My own car's design is somewhat "classic" in the design sense apart from the big Prentiss Tigers logo on the bonnet and the other one on the roof:



you can also take inspiration from the Broadwing "Patrol" preset car, which is way more classic american police car than mine will ever be, and you could google search for them
a basic formulation of classic look though is p. much stripes, numbers, letters, and the badges of whatever you are from (PD or whatever)
I also saw a kicking rad Broadwing that was a custom San Paro Port Authority police cruiser on Waterfront once but I haven't seen the guy or the car since so I never got a shot of it
Edited:
To me it's more practical to just kill them.
You can do it from range instead of needing to get close, you don't risk getting SMG'd. And once they're dead, they're dead. You don't risk getting killed by their teammates and them both surviving.
The CCG has suprisingly long range. I can fire from about the same range as my FBW or Joker with my CCG, stun them, move in and arrest, and retreat very easily as long as I time it right and my teammates aren't douchebags
I've had so many arrests botched by teammates shooting the guys while they're stunned