My wife is six weeks after giving birth and has been clean for a couple weeks already. There are no postpartum Dr. appointments available for another month which leaves us with another month not being able to do the Mitzvah. Can my wife go the Mikvah just for the sake of being clean and being able to touch, even if we will not be doing the Mitzvah for another month?
From what you are writing it seems that your wife is feeling fine, and as far as you know everything is in order, except for the fact that she can’t get an appointment for the next month. This being the case, she should go to the mikva as you write, because although it is preferable for her to be checked out beforehand, it isn’t a requisite, unless there is a reason to suspect something.