I saw a hilarious ice breaker a few years ago. The best man that went up wasn't big on public speaking either but the way he opened it, he couldn't fail after that.
He mentioned how as a best man it's only fair to let out all the secrets of the groom so that the bride is prepared for what she got herself into.
Dude whipped out one of them old school scrolls and let it roll along the floor. Started reading shyt out in point form. They were mostly one liner lies about the groom (ie: fake guilty pleasures) but shyt was funny as hell.
Allowed him to get a few good laughs in (definitely helped calm him down too), and then just went into the traditional 'how beautiful the bride is' 'being happy for both' 'honoured to be apart of this great day/night' 'wishing them the best' etc etc. You don't need it to be long. Just quick, memorable, funny and sweet, and you're good to roll. He was done in about 5 minutes but I'll never forget it.