Low-dose aspirin therapy can increase clotting time, that's a fact. However the clotting time is still generally within the normal range seen in people who aren't taking aspirin. And patients are generally asked to stop taking aspirin before elective surgery. That seems logical, too, right? But last I read (a number of years ago, but not too long), there isn't really a solid block of evidence to back up that practice. Surgeons do it because "it just makes sense". Theoretically, it's possible that it could be a problem, but it's not proven and there's a good chance that it doesn't make any difference. At this time, unless you've run across some recent research that I'm not aware of, I personally wouldn't worry about it.

That's not to say that aspirin therapy doesn't have any risks at all. It does, like gastrointestinal bleeding. It's all about balancing the various risks and the potential benefits. But if your doctor has determined that in your case, you can benefit from low-dose aspirin, then I wouldn't stay up at night worrying about the baby aspirin I took and what if I needed emergency surgery, got shot, etc. Anyway, that's my take on it.