Yeah, if it’s metal I wouldn’t worry a lot about it breaking. How long is your wrench? Support the side that goes into the wall and give it a easy going but firm twist. If it’s gunna break, then the plumber will probably break it and unless you’ve got a firm price before the job you’ll probably end up paying for the break either way. You could also try to break up the gunk with a drain snake.
You’ve probably checked this, but you don’t just have a bunch of hair in the drain stopper do you? Every time I’ve had drainage issues it was right there