I'm new to the forum; but have read a bit and you all seem to give sound advice.

I have a bit of a dilemma.
I sold an item on 8/12 rec'd payment on 8/14; When I went to pack the item (an insulated wine bag which included an ice pack) I realized the ice pack was damaged - it had a slit in it. I emailed the buyer on 8/15 and said:
" Hello,
I was preparing your item for shipment today and found that the ice pack was slit. I have no idea how this happened as it was simply sitting in a box - I would be more than happy to try to replace the icepack, or refund you $2.00, whichever you prefer. (I am very sorry for any inconvenience this may cause you.)".
To date, I haven't had a response. Should I wait to send the item until I hear back or just send it anyway? Should I offer something else?
The item sold for $4.50 so I thought a $2 refund was generous. - No?
Any advice would be greatly appreciated.