Tw sh descriptions
Painting on myself helped me with the urges a bit also what helped me a lot was setting up rules. Like, I can relapse but not more than two cuts two slices each with two days break between each relapse. With time it got a bit easier since I've not been progressing and it became less stimulating. Also helped not to make it routine.
Ice cubes and rubber band didn't help, just provoked me more. Icy showers, sudden ones without giving yourself time to get used to lowering temperature helped me too. Sometimes very slight lighter burns. It's quite hard to make them bad ones (at least for me) since reflexes make you to remove limb from heat source but it's more relapsing than dealing with the urges and not a long-term solution at all. So, cold it is for me.
Most importantly, don't involve shame in your self-harm. If you relapsed then you relapsed, it doesn't invalidate your clean strike or disappointing. No recovery is linear and involving shame only makes it harder, worse and harms relationships. If you can't stop self-harming try harm reduction, lowering sh frequency and making it less serious is a great thing too.
In my experience, what will help you with urges depends from why you sh at all. If it's just addiction speaking, it's just sth to try to wait off by distracting mind with games or sth like this. If there is self-hatred/shame/dealing with dissociation it's another story. So what works for others might not work for you and you need to study yourself and experiment a bit to find actually working way.
Btw, I've not tried drugs but alcohol is a depressant and also lowers sensitivity so it's a bad idea to deal with urges by drinking. My worst cuts I've done while drunk and replacing one addiction with another is hardly a better way.
Good luck! It's great you're trying to stop sh-ing!