Dumas preferred to ignore all the blood-and-gorey aspects of period warfare and focus on the gloriousness of it all

Yes, he does that. I was seriously considering sticking blood poisoning in my pastiche fic, but I eventually decided not to drag it on that long (basically, I couldn't come up with a good reason to keep Porthos and Aramis wandering around in the woods for an extra day, or I'd have been there with the septicemia. Walking around with a musketball stuck in your shoulder is practically a recipe for it).

I'm sure Aramis at least bathes regularly. He's got a vested interest in keeping his hair/teeth/skin/etc. pretty. And Porthos cares deeply about appearances and the importance of nice clothing--not a man to go too long without donning a fresh shirt.