Mass update for order status

Is it possible to run an SQL patch or something to change all orders in a certain order status to another order status, for example, from packing to dispatched?

Yes. Though it's not as straightforward as most updates. You would need to write a patch that finds all entries in the orders_status_history table whose most recent entry matches the ID of your packing status and use that as your input list into a query that inserts a new entry into that table with the despatched status. So you are creating new entries, not amending the ones already there.

Writing that patch may be beyond my talents or available time. Are there any walkthroughs to show me how to write a patch?
Could someone perhaps write one?

you may also want to look into a mod called super orders (available in the free downloads section). it creates a Batch Order Status update section, allowing you to, for example, find all orders that are currently set to status "x" and change them to status "y". you can also define data ranges and other criteria for the orders to be updated.