I am not sure what to tell you. I know how hard it must be for you. My AH has threatned to kill himself many, many times but only once did he actually slice his wrists and that was on his arms not wrists and I was there. So with him it ws only threats to try to control me or get me to come back home.
But my mother-in-law said she was going to and actually tried three times before she suceeded. In my experience only, take it for what it is worth, if they really want to do it they will.
Sorry I couldn't be more help. I just wanted somebody to respond to you while you wait for the more experienced cases.