At first, I'd like to say to you that your intuitions are good.
Women like casual sex the same way men does. Some do, some don't. It depends of the woman, of the moment, of the person, of the situation...
And assuming thecontrary would, indeed, be sexist.
Dating sites are actually used by a lot of women willing to enjoy casual sex. As well as a lot of women don't looking for it. And a lot of women who are okay with both.
I met a significant number of women which with I had casual sex on dating sites, as well as women which with I stayed a while (included the one with which I'm since a year and a half now). The key is to filter it.
Make it clear that you're looking for sex and not for anything else, while on the other hand exhibiting your profile (likes/dislikes, kind of people, interests, ...). Even if you don't look for a girlfriend, people have the choice and will priviledge the people that they know over those who they doesn't. While stating in words that you're running after sex would look somewhat aggressive and douchebag, andlet alone the wasted exposure for your profile, most sites have a feature allowing you to check the kind(s) of relation that you're looking for, which is easier to filter/select trough the search engine and save some space in your profile.
The next step is to be the more honnest possible and for two reasons :
Honnesty will draw a realistic portrait of you, which will look real and will have better chances to be appealing than something vague (vague description are the fruits of lazyness and/or douchebaggery).
Even if it's only for sex, you'll want to practice that activity with someone that you like. It'll make the things more enjoyable for both of you it's a friendly and with benefits relation that you're looking for.
It may actually become more than a casual sex relation (it happened to me and still last today, so I know it's always a possible "risk")
If you lack social skills, or aren't at ease with that kind of situations, dating sites can are understandably more likely to make you at ease than bars or nightclubs. If you still fail to find women interested in you in your area on the different dating sites that you try, you can also give a try to swinging/libertinism oriented dating sites. Those have a member pool way more relevant regarding your needs. The people who use these sites do so in order to find people which with talk about libertinism, share content (about them or not) and eventualy (often) have sex with.
People there are very picky when it comes to single men, since they're a lot, but still, it can work. Be polite, cool and seductive and it may end well for you.
I read in your details that you weren't willing to afford a sex worker's compagny, so I don't worry for you, but if you choose to try on some dating sites and think about getting a subscription to increase your chances, wait until you tried it for free for a significant amount of time. It'll be too bad for you to buy an annual subscription to then be very disapointed once you dicovered more about the kind of women that use it in your area, their needs and how much they're interested in you.
It's true that statistical tricks based on shared distributions, but you'll agree that a website that's used by almost nobody in your neighbourhood would be useless to you, wouldn't it ? ;)
Anyway, looking at your point of view regarding stupid rumors about casual sex among women or PUA, and the remaining, you look like a smart and rational guy. If you play it honnest, you will find what you're looking for, I think.
Also, the PUA are dishonnest, not because they develop tricks supposed to put women in their bed (I mean, it's lame, but it doesn't work on every body, and it mostly stay about dating), but because this stuff is sold to naive guys who subscribe in order to find someone which with hang out or have sex and end as douchebag. While the PUA earn a lot of money. See it like a sect...
Good luck to you !