I would like to put in a new inner wire on my Front derailleur cable. It is partially routed through my handlebars. Is it possible to just thread the inner wire through the existing housing? will I have to remove the bar tape on the handlebars?

I am guessing that the housing is wrapped under your tape, and that there isn't actually a hole in the bars. If the housing is continuous, and it probably is, then sure, you should be able to just shove the wire into one end and have it come out the other. I doubt you will need to remove the bar tape.

Sometimes I have to briefly remove the ferrule on the far end, so that I can thread the wire through the tiny hole, and then put the ferrule back on. Just as often though, the wire goes right on through.

Ah, yes! I believe you are correct about the housing being covered by the bar tape. Does the ferrule simply un-screw?

nope, the ferrule is just a light friction fit over the end of the outer housing.

One other suggestion or hint- take a real close look at all the details of the cable routing before you take it apart. Including exactly how the cable approaches and is secured at the anchor bolt at the derailleur. You can also take a quick picture or 2 of this with your cell phone etc. Getting these details just right when you put it back together is generally important to the derailleur and shifting working right, especially newer derailleurs + shifters, and especially if it's a triple on the front. (This is more true for cables on indexed rear der's, but also for front.)

Be aware that there is likely a groove worn into the cable housing by the old wire. If the new wire is a different diameter it may or may not move smoothly through the old housing. Even though it is extra work I generally replace both the inner wire and the housing together. Try the new wire first, if it works OK you are done. If you have slow or hesitant shifts, especially to smaller chainwheels you may be forced to replace the housing.

While you have the ferrule off of the housing, inspect the housing end to be certain that it has been cut or filed flat and does not have any loose strands protruding. Correct if necessary before reinstalling the ferrule.