It's not yet two weeks so it still may very well turn up.
I'm surprised you've managed to post 500 parcels and this has never yet happened.
To be honest, it's usually the seller's responsibility to get the parcel to the buyer safely. This includes tracking and insurance - it's of no concern to the buyer as long as he gets the item, but it's the seller that takes the risk and has to chase up lost packages. Unless of course the buyer has specifically stated he wants to save money and understands that he receives responsibility by forgoing the insurance and/or tracking (your buyer didn't do this).
This is the way ebay does it anyway and it seems to make the most sense, as long as you are aware of that going in.
As an honest member, unless the buyer offers to share the cost out of good will, you really should offer to compensate. After all, he's paid and received nothing.
Without insurance, you are forced to trust his word on this. After his payment goes to you, it's your responsibility to get the board to him and it's your responsibility what postal service you decided to trust.
As I say though, it hasn't been two weeks yet. I think two Months is acceptable before any refunds are given as a last resort. This way you can try and chase it up and give the parcel time to arrive. You can always come to an arrangement sooner or later than that - and you can also still try to claim insurance back for yourself afterwards.
Also, you may find that even though you didn't pay for an insured service that there is still some insurance included for lost items.
In answer to your questions:
1. Agree to a wait and hope timespan based on recommendation from the post service and then offer a refund.
2. If I were you I would kick myself for not sending it tracked or insured.
2b. ...But then I would remember '500 parcels uninsured. I'm still up.

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