[Face Up.]

I think that you've covered basically everything you need to here!

They may not know what they can do to help though, so one thing you can do is tell them some things that WILL help you, and some things that WON'T. For example, if you think one thing that will help you is being there to talk without being judged, tell them that. If you think taking away your tools won't help, say that. At least then they'll have something to go by.

If you think they won't understand self harm, you can also print out pamphlets or get other sources of information that will help explain it.

If you think it will be easier you can tell them in the form of a letter so nerves and interruptions won't get in the way.

It is awesome that you want to tell your parents, though, and I hope everything goes well! You are making the right choice here.