There is an inner axle shaft on each side. The birfield is sometimes referred to as an "outer axleshaft.
Unless you are a skilled and knowlegeable mechanic yourself, capable of diagnosing and repairing the problem yourself, never take your rig to a mechanic and tell him what to replace. He might do just that. Whether it is the actual problem or not. And you will have little to complain when the actual problem is not fixed. Tell him what the symptoms are and let him determine what need to be done. Put that responsibility on him. It is part of his job. You want the problem fixed. Just replacing some particular part that may or not need it does nothing for you. IF he is not capable of diagnosing the problem... he should not be working on the rig for you.
$1000 is cheap for just the labor for this job. Book time is 2.5 hours to replace one inner axle shaft. If the axle is not grooved from the seal wearing it, then it would not need to be replaced. Still has to be removed for inspection. If it is grooved, just replacing the seal will not solve the leak. Either way the time would be the same. There are offset seals that are available and there are sleeves that can be used to address a grooved axle without replacing it. Neither of these affect the labor time. (Actually, installing a sleeve will add a small amount of time.)
The clicking is from a worn birfield. Replacing or not replacing the birfield will not add any labor time. Not replacing it will of course not stop the clicking (or eventual failure of the birfield).
This job can not be considered complete without replacing all the contaminated grease. It can not be considered first rate without inspecting and possibly (probably) replacing the wiper seals as well as the inner axle seal and the knuckle and wheel bearings. The time to do this is not included in that 2.5 hour figure.
Edit: Also, if one side has problems... both sides need attention. They have the same mileage and the same wear.
Mark...