Changing one product permalink

Not without changing all of the products.
This may not be what you want, but you can add a has to the end of the url.
window.location.hash = 'something';
That would print out as:
mysite.com/shop/uncategorized/myproduct/#something

Again, it isn’t what you wanted, but it is atleast someway to separate the likeness between products. You could change ‘something’ to something more related to whatever products you are referring to. Honestly, I don’t feel like this is a good solution, I’m just trying to give you something.

I looked into that as well before I posted and couldn’t find anything. I hope you can. If you somehow do, be sure to comment here so that I and everyone else knows how you did it. It would help people in the future.