Is it permissible for an unmarried woman to bypass her ill-reputed and uneducated paternal cousin when her marriage contract is being solemnized, and to appoint another elder from the family, and are there reasons that allow this, and would the marriage contract be valid in this case?

It is not a condition for the marriage guardian (wali) to be equal to his ward in knowledge or wealth, nor is justice (adala) required in him according to the majority of scholars; because his فسق (open sinning/immorality) does not nullify his guardianship. However, if the closest guardian prevents the marriage without a legitimate شرعي (Islamic legal) excuse, his guardianship is forfeited and transfers to the next in line among the guardians. If all the guardians prevent the marriage (عضل), the ruler (hakim) assumes the responsibility of marrying the woman.