If you care about Sturmey Archer hubs enough to have asked this question, you should just give in and do it yourself. It's not rocket science, and you don't need any special tools. The AW hub in particular is easy to deal with. Granted, there may be worn out parts in your hub, in which case you'll have to find replacements, but for now, don't worry about that. Find the instructions online, clean off the kitchen table, and go for it. What could possibly go wrong?
To answer the last question, if you totally eff it up (which is unlikely) you may have to bag up the loose parts and send it all to someone. Probably not. Worth a try! Go for it! We'll be here cheering and offering useful advice, I promise.
This is good advice. It's not even that difficult compared to, let's say, a car or motorbike gearbox.
First, find yourself a Sturmey-Archer maintenance manual. These are available online:
... and find the AW diagram:
(the AW changed slightly over the years)
Take it apart, removing the ball ring is the trickiest: SA recommends you use a flat screw driver and hammer.
Clean the shell:
Clean all the internals:
I use mounting putty to get the dirt out of hard-to-reach places:
Reassemble the internals on a vice. The most difficult thing here is getting the fiddly pawl springs in place:
Fill with the recommended amount of motor oil and you're done:
Follow the diagram and it's pretty straight-forward: about an hour's worth of effort and you'll have the satisfaction of having done it yourself.