Sort Posts using Dropdown with Custom Fields

I’d like my readers to have an option on how to sort Category pages.

I have 2 dates on each post, the translator’s date and the original post date. Right now, it’s sorting by original post date which is a custom field called date_value.

Ideally, I’d like to see something like this. Nothing fancy, straight up HTML without java script would be great!

I saw a thread trying to achieve what I wanted to do as well. But I have no idea how/where to implement it! If it’s possible, sticking to the functions.php file would be the best.

Thanks a lot, everyone!