Is it permissible to marry a married man who wishes to divorce his wife for personal reasons, while fearing injustice to the first wife?

There is no impediment to your marriage to him, whether he divorces his wife or not. This is not considered an injustice to his first wife, as polygyny is permissible for those who can be just. You have no relation to his problems with his first wife, and you do not sin by marrying him, provided that you do not ask him to divorce her or encourage him to do so. If he does not divorce her and wishes to marry you, he must be just between you both. Otherwise, polygyny is not permissible for him, due to the Almighty's saying: (But if you fear that you will not be just, then [marry only] one).