According to this page, the threads should be 4mm x.7mm. Common Yoyo Axle Sizes
I agree with @jhb8426 though, the tap and heli-coil will probably cost over the price of a replacement yoyo, not to mention the fact that there’s a pretty good chance of screwing up the job without the right equipment and care.
With that said, if you do happen to decide to toss your Shutter and replace it I’d be happy to take it off your hands for the price of shipping if you’re in the U.S.! 
I don’t own the tap yet and am not particularly skilled at machining but I’ve been wanting to try and heli-coil a yoyo for science.
If you decide to go for it, let us know how it turns out!
Ivan