YOu're really lucky to have the scottish accent. There's loads of scot songs I'd love to sing, but couldn't do convincingly due to the dialect.
The Highland Widow is a nice song, and would suit the accent well.
As far as shaking goes - try the banana trick much recommended by harpists on this forum. Apparantly they are natural beta-blockers and will help you stay calm & collected. That will probably help with the breathing too.
Forgetting the words can be a self-fulfilling prophecy - but one thing that really helps is to have a little bit of paper with just a key word or two for each verse to jog your memory. Then you can just glance down & remind yourself which bit is next. You'd probably find that you didn't actually look at it anyway.

Kris