Do you need to mention sick pay at all in the contract? Statutory Sick Pay would apply by default and due to not meeting the AWE (average weekly earnings) your nanny would not qualify for SSP, so in the event of a illness lasting more than a week you would give them form SSP-1 and tick box E (for not meeting AWE). SSP-1 has to be given within 7 days of them going off sick. So by the time you started paying something towards their sick pay, they would already have form SSP-1 for claiming benefit.
So I am thinking that you could instead pay for the first three sick days, at your discretion. You could pay for a longer period but I think your nanny would have to declare the payment they are getting if they claim income-related ESA or Universal Credit.
It could all get complicated with regard to how your payments to your nanny then affect any benefit claim they have. So I would try to keep things easy and pay sick pay only at your discretion, not contract yourself in to having to pay something.
I don't think offering your nanny 3 days of sick pay only in the event that they are off for a two week period, or some arrangement like that is going to make a difference to them accepting the job.
So if they are sick, then you decide towards the end of that pay period (such as towards the end of that month) if you will pay any sick days or not. So if your nanny works for you for 8 months and then has a sick day, you can choose to pay it. You are not tied to the contract saying that first three days of sickness are unpaid. If your nanny keeps taking time off sick, you can stop paying sick days at any point you determine, not a point the contract says.
So contractually I would put 'SSP only' so you can do what you like in the event that a period of sickness occurs.