I have been a woodworker for 50 years. In the early days I did carpentry work for a construction company but mostly I have done it as a part time hobby. I have never smoked and I have good lung capacity at age 65. However, at the insistence of my wife, I have gotten serious about dust, as of late, and I must admit the more research I do, the more concerned I get.
I think your idea of building a wall between the workout area and your shop is a good one. Put door seals in place and it would seem you will be just fine for workouts. If you wear a good mask while working in your shop, you should be in good shape but remember the dust can persist long after you stop using the tool that made it. Depending on the tool you may need to keep the mask on a few hours afterwards (assuming you remain in your shop). The particles we must worry about are smaller than 10 microns and typically the human eye can only discern particles that are 29 microns and larger. So even though an area looks dust free, it probably isn't.
If you can afford dust extraction (rather than mask alone), go for the highest horsepower extractor (mine is 3hp) to get high flow rates and the best performing filter you can afford. Please note, I have a mid sized shop 10m x 8m so I need to install ducting and a stationary dust extractor to reach all of my machines. The more ducting, the more friction loss, thus more power required, etc. If you set up a portable dust extractor for a single machine (and thus little distance between extractor and your tool) as long as the flow rate is circa 1000 cfm at the tool you should be OK. Add a good filter (3micron or less) and you should be in good shape for a long time.
Don't be too discouraged about this subject. I must say the feeling of achievement from creating something from your own drawing to final form is incredibly fun and enjoyable. Plus you are creating something useful and growing your skills with each project. One of the things that my wife finds attractive about me is my ability to fix, repair or build almost anything. Surely, this is a far more productive way to spend spare time than watching the tube or playing video games and some women even find this an attractive quality.....