I don't think most phone companies would see giving out the Line Identifier number as a major security issue.
I've had an operator in Ireland give me the code over the phone so that I could figure out which line was which coming into my house. It probabally presented more of a security risk in the old days when phreaking was still possible and switches were still crossbars, step-by-step etc.
Calling your mobile phone from the line is definitely the simplest sollution if you don't have / don't have access to the number.
However, I would suggest giving your phone co's tech support/repairs number a call and asking for it explaining why you need it. They shouldn't have a problem giving it out.
