Some responses, etc.
1) I have a shop vac. It is very noisy and bulky. I do not consider it to be an acceptable solution for the problem. Also, it requires an additional item (with what I suspect can be a very high current draw) plugged into my already very convoluted power set up.
2) Don't have a DC, hence the reason for this thought. Yes, that would be great, but like the shop vac, don't really have the outlet to spare. Or the room for one.
3) A system working off the lathe, which is already running and plugged in, may not be able to supply even marginally close to the power of a DC or even a shop vac, but it would (hopefully) supply something. And if it can reduce the amount of fine dust that ends up laying across pretty much everything in the garage, that would be a good thing.
4) If set up properly, there is no inherent risk to this idea. It would be designed to move air, which in turn would carry the fine dust.
Shop vacs and DCs have no part of this idea. They are out of the question. Will it prove a viable solution? Maybe not, but the construction costs should be minimal. (And, besides, I do have a turbine from a fighter jet that I can use for the impeller. <- Kidding. Yes, I have one, no I wouldn't use it.)