LOL our best man dressed up as Elvis and sang I cant help falling in love with you for us!
That's really sweet.

I still think the bit in Love Actually where the best man organising musicians to sing/play 'all you need is love' That's awesome.

We had an old fashioned theme for our wedding (check out the photos on FB), so our music reflected that. Our dance was 'Sway' by Dean Martin.
I walked down the aisle to 'Po Kare Kare Ana', a Moari love song
During signing we had 'What a Wonderful World' by Louis Armstrong and 'When I fall in love' by Nat King Cole
At the end of the ceremoney we had 'I feel good' by James Brown along with a confetti cannon

Other songs we thought of using included Aerosmith "I dont want to miss a thing' and 'Stand by me' but we wanted to stick to our theme.

Re: the Tim Minchin song, it's sweet and made me tear up. If it works for you, use it.