You want to make contact. How depends on the distance and convenience of doing so. If you worked in the same building stopping by would make a lot of sense. If you have to drive an hour in the middle of the workday, that might not make as much sense.
A phone call can be a nice compromise, you can be confirming the email address, or confirming the position description while making the initial contact. You can also ask what the next step in the process is. That will let you know what their time frame is for making a decision.
The cover letter can be used to show how perfect you are for the position, but that is hard to do if you don't know what the position is. The cover letter can be used to remind the manager who you are, how you know them, and who requested that you contact them. In this case you are using the cover letter to offer up somebody as a reference because that is the only reason why you are being considered.
Even if you deliver the CV and cover letter by hand, expect that they will want an electronic copy. Most companies will want to pass the resume to the proper person for the hiring process. They may want to store the document for a few weeks before making the decision.