Most of the pumps I've seen have a pair of rubber seals on the shaft-
one to keep the salt water inside the pump and the other to keep the
oil inside the engine. As you've observed, leaks generally drip from
the gap in the pump housing casting.

As long as the leak is small, this is not a huge problem. However, it
won't cure itself and will only get worse. Once the seal fails
completely, you won't have good cooling flow and you will be stuck.

This is generally a pretty easy repair, once you get the pump separated
from the engine. Be sure to have the new seals in hand before you start
the repair. Depending on the age of the pump, and the amount of grit in
the water, the shaft may be scored/worn in the area of the seals.
Sometimes (eg if you are not near replacement parts) you can polish
this up with emery paper so the new seal will not be trashed.
Otherwise, you should replace the shaft while you have the pump torn
down.

There are a pair of bearings in there as well- getting them
on/off/replaced without messing them up needs some patience and the
right collection of tubes/sockets, etc to drive (or press) things apart
without trashing the bearings. Sometimes you can do the job without
having to mess with the bearings- assuming they are ok.

Water pumps and impellers are a common failure/wear area, so probably a
good place to start doing your own repairs. If you're nervous, you
could save quite a few dollars by just pulling the pump and taking it
along to your mechanic so he can do the job on his bench.

I've done this a couple of times on my Westerbeke- fortunately both
times tied to a nice quiet dock!

John