Given the comments above, I would suggest something like: There is an important class I would like to attend. However, the class meets on Fridays, which is during my scheduled work time. If you would be willing and available to work my shifts on Fridays for me, I would be willing to work your shifts on Tuesdays. This would mean a lot to me if we could swap our working days. You also might want to mention how many weeks the class goes for, to give the person an idea of the duration of the swapped schedules.

I want to swap permanently because I want to attend an important class.

Hi there, the English there is good grammatically but text itself is a little sparse, so here’s some questions for you. Do you want him to swap just for one week or is it permanent? Why do you want to swap? Anglophone cultures aren’t always the most direct, so it might be worth saying “I’d appreciate it because...”. If he knows why it might be beneficial for you then he’s more likely to swap, whereas if you’re asking him to give up a long weekend just because you’d rather have it...well that might not go down as well.