Praise be to Allah.
If the system will indeed excuse you from going into the army, then there is nothing wrong with seeking the help of someone who can get you out of that. If the matter involves paying money, then it is subject to further discussion:
1 – It is permissible for the intermediary to accept money if it is not in the nature of his work to check who is fit for the army and who may be excused. But if that is part of his job, then it is not permissible for him, because that comes under the heading of bribes and haraam gifts to workers.
2 – It is permissible for you to pay the money if you cannot get your rights otherwise. If it is a haraam bribe, then the sin is on the one who takes it only, and there is no blame on you, in sha Allaah.
And Allaah knows best.