Would you accept 'some string'? I can't think that I'd ever say 'a string' or 'one string' in English
"A string" or "one string" is completely natural in US English.
Native U.S. English speaker here, & I agree with CroverA. I can't think that I have ever heard someone say they need a string, unless it's for a guitar or violin.
I believe in this sentence, it is the same in Norwegian, a string for a guitar or violin. So all is good :)
Except in examples like the guitar string mentioned, I would usually ask for "a piece of string" in BE.