I don't charge for sick days or stats. I charge the very high end of my area so this is the main reason clients sign with me.
I also have something in my contract that states that a client may take off one full week without pay only, everything after that must be paid in full for the week. This stops clients from taking multiple weeks of vacation, or if a child needs surgery or is ill for a week that's it for the year.
This system works for me. I don't charge for sick because I don't want a client coming sick because they feel they have to get their money's worth. If you sick, I encourage you to stay home.
Yes, I'm sure some clients do fake sick in order to get an unpaid day, but I haven't experianced that yet.
I would not give the client the option of sick or stats, it's your business you should dictate. Don't give the client too much control.