select some words or phrases from the earlier lyrics
la la
fa la
hum
whistle
small instrumental solo

I know what you mean. I cringe at "twiddle dee dee dee" in Mockingbird Hill. And when I play 'Buttermilk Hill' on my dulcimer, I substitute an entire improvised verse for the nonsense in the Peter, Paul and Mary version. Bibba bibba boo - give me a break.

But perhaps you want to keep the vocables for some reason. We all know that some syllables are more twee than others. Feel free to change those you don't like to something else.