Well - let's start by putting this in perspective. You say that you don't want to develop cancer (none of us do). However - your odds of developing cancer of some sort just by walking around and living your life outside the boat yard is about 40 - 50% (about 1 in 2) and your odds of dying of that cancer are about 20 - 33% (about 1 in 5). There are other, non-cancer endpoints that may concern you as well. What you're really concerned about is the excess risk of health-related problems posed by living around a boat yard.
As others have mentioned - health-related risks are generally posed by inhalation of dusts or vapors. The skin offers pretty good protection against threats posed by direct contact with air-borne dusts and splashes (just don't let the contaminants sit on your skin for extended lengths of time). Likewise - nose hairs, mucus and other things help protect against the inhalation of dusts. Vapors enter the body by breathing - and transfer across membranes (like the eyes). Fortunately - membranes do not compose a significant portion of our exposed surface area.
Let's turn our attention to breathing - we take about 20,000 breaths per day. So ... what proportion of those breaths do you take when you stroll through the boat yard? If it's a significant portion (say, you jog around rather than walk directly through, or for some reason you walk through the boat yard many more times than twice a day,
etc.) then you're increasing the excess risk - but not by much.
As MikeHoncho has said - it's impossible to put a number on the excess risk if we don't know what concentrations of which contaminants are in the air that you are breathing.
So - we'll look at how to minimize the excess risk. Is there only one
live-aboard marina convenient to you? If not, and you have a choice of
marinas - then see if any have a prohibition against
sanding without a vacuum/filter. You could also get a wind rose of your area and make sure that the location of your slip minimizes the exposure to wind-borne contaminants. Make sure that your slip is as far away from the working area as possible. Wear a mask (certainly, most of us are used to wearing one by now) as you walk through areas with dust.
If you do the above, your excess risk will most likely not be above 1 in a million - so instead of having a 0.5 chance of developing cancer you'll have, by virtue of living near a working boat yard, a chance of 0.500001 of contracting cancer. Can you live with that increase?
[There are, of course, shorter-term organoleptic responses, but these occur generally quite quickly. So, if you haven't already broken out in rashes or sneezing fits by touring the boat yard - chances are good that you won't have those types of problems].