Overdue shipment

Okay, so I had a buyer purchase something from me almost two weeks ago, but I only saw the notice today, and obviously it says the item is overdue. I freaked out and contacted the buyer to apologise, saying I will ship it express tomorrow, or would otherwise offer them a refund.

 

The thing is, I haven’t heard from them at all. They haven’t been in contact asking where their parcel is, and I haven’t yet received a response to my message.

 

What is my course of action here? I don’t want to ruin my seller score, but I’m not sure if the purchase just slipped the buyer’s mind. Should I just go ahead and ship the item or wait for confirmation? 

Thanks!