It's up to you. If the buyer wants it badly enough to pay the shipping it might be worth it, but you are likely on the hook if they want to return it.
You really shouldn't let buyers talk you into changing your listing like that, all too often it ends badly. If you don't want the "hassle" of shipping don't do it, you don't have to if you don't want to.
Local pickup items are not covered by the MBG, but in some cases they can be returned for a refund. The blues have posted before that ebay will force refund/return on local pickup under some circumstances.
If you DO decide to sell to the buyer, REVISE THE LISTING to include a shipping option that correctly covers the shipping cost + fees + packing supplies, etc. If the item has already sold, do not ship it as you have no guarantee the buyer will pay for the shipping, they either have to request the order be cancelled and relisted with shipping or that you cancel the order (use problem with buyer's address, they aren't local so they don't qualify for local pickup) and relist.
Member of the Grumpy Old Man crew
