Here are some ways NOT to introduce your song/tune/poem:

"I don't know this one too well, but ..."
"I apologise in advance if this goes wrong ..."
"Okay, let's give something new a try ..."
"I'm still working on this ..."
"Here's a song I've been trying to learn, it's quite difficult ..."
"This was fine at home, but well, let's see ..."
"If this doesn't work, I'll try another one ..."
"I'll never do this as well as the original, but ..."

No!!! Just smile, introduce it confidently if you need to introduce it, and then go for it!

If you make a real hash of it, well, we've all been there! Then you can just laugh it off with a joke, and try to sing your next song better.

No one but you really cares at all that you messed up, and neither is anyone but you likely to remember!