Is there any religious impediment to the wife's father appointing his brother (the wife's paternal uncle) to utter the words of proposal (ijab) and acceptance (qabul) in the marriage contract, knowing that the father is the guardian whose name is written and who signed the official documents, and that the uncle was recorded as a witness?

It is permissible for the guardian to delegate someone else to marry off his ward. However, the delegated person's testimony to the contract is not valid. The criterion is what transpired during the contract. If two just witnesses were present and heard the offer and acceptance, the witnessing of the contract is complete, and it is not a condition that their presence be with the intention of testifying. Based on this, the aforementioned marriage contract is valid.