Here's my thoughts, which are worth exactly what you are paying for them.
BIL called me the other day and said his female friend's wanted to get a Shield EZ .380 without an external safety. I asked why they had chosen that? He said EZ for easy to rack slide and .380 for low recoil. And no safety because they read on the internet a thumb safety will get them killed.
My response was can't they rack a regular Shield? "Didn't know hadn't tried."
Is a 9mm to much recoil for them? "Didn't know, they don't have strong wrists."
As far as the round goes I think a .380 is useless. But that's just my opinion based on my experiences; others disagree. A 9mm would be a far better choice if they can reliably handle it.
Will they carry it in a purse? "Probably". A semi-auto being carried in a purse would have to be in a holster that would cover the trigger with absolutely no chance of it coming out. (Thumb break). Especially with no safety. Anything less and someone may get shot.
I suggested they check out a .38 revolvers. Still needs the trigger covered, but far less chance of something hitting the trigger and firing it.
Or a SCCY 9mm. Double action, with a 9lb trigger pull.
I told him I have a .38 S&W J-frame, a SCCY 9MM, and a .40S&W Shield (If they can handle it; they can handle anything). Come by and get them and take them to the range. Rent an EZ while there.
I also told him to tell them to do their "internet" research on the .380 EZ. I've never shot one, but when they came out there was a bunch of owners posting about ejection problems. They were desperately playing with magazines springs and such. My opinion; it's the .380 round. They didn't seem to have that problem when the 9mm EZ came out.
But the bottom line is that they need to shoot before buying, or they probably won't be happy. They need to know they can handle it, and they need to know they can carry it comfortable. Otherwise; it won't get carried. They also need to be trained, and they need to learn how to safely carry.