I'm afraid I'm completely the opposite! Well, "what services do you offer" just gets them directed back to my website, cos really if they don't read everything on there then there's no hope for either of us. But "are you working today?" is, in my opinion, preferable to, "Are you open today?" or "Can you squeeze me in?" or "Is there a slot available?" (That last one literally curdles in my ears!

"Slot"!!!)
But frankly, as long as they aren't calling to waste my time (by clearly being more interested in a long phone conversation than in actually arranging a booking), I don't care what wording they use. Some guys are more casual ("Are you free to meet later?") and some guys are quite formal ("I would like to arrange an appointment with you, please") but as long as they're talking about booking logistics, I'm happy!
I know it can be slightly annoying when someone else tries to tell you something about yourself, so please don't think I'm doing that here when I mention that usually, the only thing that makes me irritated every time my phone rings is burnout. Burnout doesn't have to be caused by doing 2000000000 bookings back-to-back, either; I find it's usually a result of needy clients who try to book every week, plus lots of idiotic calls that make me question the progress of humanity as a whole, combined with the unlucky thing where all the nice, genuine callers seeming to want to book when I'm not free. That lot of stuff is just stressful and can result in nothing but difficult bookings and lots of time wasted, so I end up either wanting to yell or sob down the phone every time it rings!
Sorry, that might well not be the issue here, and if so it's off-topic. It's just that I don't entirely understand what you're getting at in your post cos those lines are fine by me (except anyone wanting too many details, as mentioned above) unless, as I say, I'm just in a totally frustrated and worn out mood anyway. And to be honest, I prefer clients indicate that they understand that I'm working and that I'm doing my job when I talk to them and when I meet them; these guys are less likely (in my experience) to turn into "Since you enjoy having sex with me so much, Emily, I've decided to stop paying you and to start calling you 16 times a day just to see if you fancy going for coffee" (aka completely insane) guys. I'm guessing your experience is completely different, though?

In which case, I would probably say that as long as your methods for screening out the clients you don't enjoy seeing are working, then I completely empathise with the frustration with all the other weirdos who just keep trying, day-in, day-out, dozens and even hundreds of them, a never-ending army of odd'uns with far too much time on their hands, etc etc! - I find that completely wearing, too.
But I wouldn't personally turn someone away who mentioned "services" or "working", as long as they weren't trying to turn the conversation into free sex chat. If you're wary, perhaps answer them politely and say you'd love to see them, but implement an extra step into your booking procedure? Tell them maybe to email you with the time, date and duration of booking they'd like, so that you can pop it straight into your Google calendar (that's an excuse, of course; the real reason is so you can assess how genuine they are and whether they can follow simple instructions without turning into stroppy teenagers!) - or if they email, tell them you need to receive a phone call from them at a mutually agreeable prearranged time to confirm, for the same reasons of 'testing' them slightly.
If they do follow your instructions - and you have your security sorted with a buddy who knows where you are and who you're with and when you'll be finished - then it might be worth going ahead with the booking. Always keep an eye out for any other weirdness, of course; it sounds like you're more than proficient at doing this but you know how it is. Just take that little bit of extra care at first. It's added stress but it could reduce the stress of missing out on perfectly good bookings, if it works out!
