How do I control the smoke from a chimney starter?
First off, I'd cease using paper as your tinder. While it is the cheapest way to get your charcoal started, it does create a lot of smoke and ash flying around. And avoid oil-soaked paper. This will create even more smoke (I speak from experience).

I started using firestarter cubes, as they burn hotter and longer, meaning my coals are ready for cooking faster. Also, another side effect has been that the only smoke I see is from the charcoal itself. I started using the Weber ones, but they are expensive and don't burn as long. So I switched to a different fire lighter. You'll have to forgive me, as the name escapes me -- once I get home I'll edit this answer with a picture of the bag. Anyway, they're cheap, at about US$ 5-6 for a bag of 72. And they burn long, hot, and smoke-free.

The only remaining problem you'll have is that when charcoal begins igniting from a low starting temperature, it puts out quite a bit of smoke. If you are still worried about smoking your neighbors out, you will probably want to experiment with different brands and types. Stubbs briquettes are a bit less smoky on ignition, as is most lump charcoal. If you use lump, though, you should make sure you pack the charcoal ring in your WSM nice and tight, or it will burn very hot and fast. Also, put a piece of expanded steel on the charcoal grate to keep the small pieces of charcoal from falling through.