If the guy is coming that week anyway for her birthday then that will put your friend in a horrible position. She will either have to cancel on you or leave him on his own for the day. Will one more person really make a difference?
Going to a wedding dateless is not so bad. I met my fiance at a wedding so quite glad i attended it on my own really. I do get what you mean about not wanting a bunch of people you don't know at your wedding. I have had similar issues with my family and do regret not putting my foot down a little bit.