You do need a wali, but like you said if the wali is acting unreasonable i.e not allowing the girl to marry because the man is a different colour or caste then the wali becomes a relative.
Is the caste thing the only issue your parents have?? Would they rather marry their daughter themselves to someone of her choice or would they like it if she ran off and married without their approval.
My parents and cousins were like this but now times are changing and so have they.