Personally - traditional tuxedo and bowtie (which are cool, btw). I might have something Trek hidden on the tux or in the church, definitely on the groom's cake. But the wedding for me would be as traditional as possible. I just thought this guy had an incredibly well made dress uniform.
Why be embarrassed? If it's not something you would do, fine, but why feel anything when someone else does this? I'd never do it myself, but I don't care if someone else does it.
This and this.
I'm not sure what kind of Trek things I'd put in my wedding. Probably something a little more than just a hidden thing here or there but really not anything too huge... I wouldn't really want anything too over the top in the first place because I'd already be uncomfortable being the center of attention.