Because you have selected "Strict" as your cancellation policy it means that any deviation from that will have big consequences for you or guest. I agree with Helga's strategy but you might consider first asking the guest to call airbnb to see if they will cancel for them if they are informed that you agree to it. Probably they won't refund their own fees but in general it feels like airbnb is bending over backwards to accomodate guest requests.
You'll come across this each time you have someone who wants to cancel under "strict", it is meant to be a serious committment from both sides. However be careful if you change because it has been the case lately that some hosts are not able to return to a "strict" policy if they change it to a "moderate" policy.
In general, it isn't about them not wanting to support you as a gracious host as much as enforcing the big committment that strict indicates.
Best of luck, let us all know how it turns out!
Bridget