You should care. Bigger risk of getting a bad reputation.

Take extra care to not be creepy. Look attractive. Dont just hang around the same spots. Be outgoing and social with random people in general, not just with hot (esp. young) girls.

Consider a modified version of it that's less ... "cold" - by which I mean, look for an IOI, or try to position yourself to get one. Don't just walk up to someone who doesn't know you're there.

Here's an example from a movie: https://www.youtube.com/watch?v=-hNbw5_HnC0

He gets the extended eye contact (an IOI), then he walks over to her and says, "do we know each other." This is as opposed to walking up to her without the IOI and saying something like, "hi, my name is Brad, I just thought you were attractive" - that's a line that going to blow her ego into the stratosphere.

My go-to these days, if I get eye contact and a smile, is "do we know each other" or "have we met" - it's been working pretty well.

Next, what I mean by "position yourself to get one" is to look for opportunities to be in someone's line of sight or just to get their attention without specifically talking to them. Here are two examples:

(1) I've started collecting "local artists" - by which I mean, I find someone who plays gigs at cafes and bars, and I try to go listen to them. I look for chill music like acoustic guitar. I don't want anything that makes it too loud to talk. So, I'll listen to a set maybe every other week, I'll drop some money in their hat, and eventually they'll recognize me and say hi, and I'll acknowledge that I've been there a few times when they were playing - say something like, "yeah I've seen you play three or four times, I really like it, it's a great show" - so, just friendly, complimentary banter.

What all of this background work eventually gets me is, if there's a hot girl in the bar, I can talk to the artist on a break or before/after a set - just more friendly banter, asking how they're doing etc. And every time I do that, I know for a fact that the hot girl has seen me.

Then when I approach her, I'm not a random stranger, I'm that guy who is friends with the artist. It's less "cold"

(2) Saying a joke out loud to no one in particular is a great way to get noticed. If you don't get a laugh, no big deal. It doesn't count as an "approach" - but if you do, you can introduce yourself and then it's not "cold"

I like going into the grocery store, going to where the limes are, picking one up, and saying, "wait why are these lemons green??" or picking up an onion and saying, "why does this apple look weird?" In a bar, if I order a beer and the bartender sets it in front of me and then goes, "this is 8%" I say, "8% what?? Is there alcohol in this root beer?"

Basically, I make a joke whenever there are people around. That's how you get comfortable enough with it. You'll be surprised how many people will crack up at random shit like that.

Is there any proper way to go about this, or should I just not give a shit?

yeah, just do it.