In general, minor exposure to any carcinogen doesn't affect you much - it's the prolonged heavy exposure over months and years that does the trick, along with a bunch of bad luck. Of course this doesn't mean that you should ignore safety, but there's no reason to panic over small doses of this or that.
And yeah, cured resin is chemically very stable, so it's mostly the general dust effect in the lungs. Unmixed resin components can be carcinogenic, though.
For our auto mechanic friend, I'd recommend this type of goggles that have soft sealing edge and an elastic strap to sit tight. Pretty optimal when you're working in weird positions - and also good for riding Harleys