When making ice, add red food colouring. Then you get two different things - you get the pain from holding the ice cube but it is also red and looks a little like blood when melting. x
Something liquid like red ink or red food colour is worth a go.
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But I think I know what you mean. Blood has a specific symbolism.
If all else fails make the cuts as shallow as you possibly can. Or draw blood by pricking your thumb with a sterilised needle. You have no reason to do anything that needs even plasters.
Please note that I'm only suggesting this as a step towards stopping, not saying it's OK. I have personally not cut in well over a year now.