EDIT: I realized my initial answer on hashbang didn’t answer your trailing slash question.
To remove the trailing slash on ALL URLs: Add a rewrite directive to the server block of your nginx config file that looks for URL’s ending with a trailing slash and permanently redirects to the same URL without the slash:
rewrite ^/(.*)/$ /$1 permanent;
To remove the trailing slash on ONE URL:
rewrite ^/page/$ /page permanent;
Keep in mind nginx never actually sees the