I film with nothing but my phone in my hand.
It’s really about acting natural. Subjects will notice the shooter first, not the device first. The shooter is who will set off alarm bells not the device. It’s once the shooter gets noticed that they start noticing the device you’re trying to shoot with.
Heres a short clip of me holding my phone in my hand standing right next to the subject facing me while I start by capping her orange painted toes poking out her sandals then up for a faceshot then rotate the phone to get boob, hip and crotch shots (her boobs and hips were what got my attention more so lol). Very little motion involved and o had the phones back camera filming and she didn’t notice nor react.
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But what you can do if that’s a bit too much to start is to put your phone (I’m assuming you’re using a phone) in a side pocket of a bag (for example) and then place the bag down by the subjects feet to cap.
Down and dirty is just starting recording right before you lower the bag down to foot level. But what would significantly help is if you have a smart watch or another phone and remote link it to your shooting device. Then you can actually see what the recording device is aimed at, make adjustments by nudging the bag a bit, then remote start and stop recording . This method will allow you to get the closeup foot shot and depending on how you angle the bag and pocket you could get that fisheye upward tilting caps (which I’m guessing is what you’re talking about).
As far as hiding the phone screen? Yes you can use a BVR app (it’s an app that allows you to secretly record while it hides the screen or replaces it with another screen) but what those apps capture isn’t as good as the native cam app. So instead think about using a phone wallet case which will cover the screen.
PS: I use a phone wallet case and shoot with the native iPhone cam app.