When I used to cut my legs I would take a cloth and put it on the inside of my pants and underwear to cover the cuts. Sometimes I would wet the cloth with water to avoid scabbing. This may lead to infection though so ymmv. It worked for me though and with a little bit of luck my scars have faded signifigantly over time. However they are still visible and will be for the rest of my life. Not that it matters to me much anymore, but it did at one time.
Keep the cuts clean and covered. Use a sharp blade. Prevent scabbing. Do that and no one, but you, will know. Unless you decide to tell someone. Unless you know that you're going to get help, I'd recommend not. But hey, you do you.