Wakil: Is any person who is legally appointed by the Wali to represent him in a situation like marriage: In this case he is basically ordered to say whether the wali is accepting the marriage or refusing it.
This means either the father is needed to be present during the 'aqd an-Nikah or he needs to be represented by his wakeel!
So if the option of a wakeel is available the father just need to appoint him by a letter in which he (if necessary) even make his "acceptance or refutation" clear and the most important content of this letter is that this wakeel is clearly appointed by the father (for example by an IDCard# or anything that would help to clearly identify him).
Else if the father refuses for no good reasons ((For example the boy is not a practicing Muslim or drinks alcohol etc.) the girl can go to a shari'a court and ask them to take the guardianship away or repeal it from her father.
Note that however this might be a legal and permissible option it would be a time-killing act especially if the judge is not willing or accepting to do so, except if father is really out of his mind, for any reason and don't want to let his daughter get married at all.
To be honest an Imam or judge can be a guardian if the father is not present, but no Imam or judge who knows the rulings of Allah well would accept this duty if the guardian (father) of the (born Muslim) girl is alive! A clear exception is the case of a convert girl, as non-Muslims can't be guardian for a Muslim woman (but in case of marriage among women from people of the book the rule of guardianship applies), here it's usual for an Imam or Judge to play the role of the guardian.