How to make a player actually invisible to mobs and players with its armor

I wanna make a hunter armor, which turns the player invisible when sneaking. However, the invisibility potion effect only hides body parts, and not armor, so the player is visible to mobs and players. I wanna make it so that you can become actually invisible while still wearing the armor.

I also wanna make him able to walk faster while sneaking, but this isn't doable via the speed effect, as it only works if ur running and not sneaking.

So, if you know how I could do that, please help me out.