Agree very stressful when your offspring do stuff in public! I had my heart in my mouth when DS made his speech at his wedding earlier this year, not least because he had teased me and said he was planning to 'wing it'. In the end, he stood up, folded out a long sheet of paper and made the best speech ever: made us laugh, made us (and his bride) cry, and generally did not put a foot wrong.
When I said to his sister afterwards, "The b*gger, he said he was going to wing it", she replied "But, he did! There was nothing on that piece of paper but a list of names". 
Not that that compares to live TV or Strictly though, so I can imagine, I'd be a wreck.