If you specifically want to go the picture-in-picture route, see how webcam works in Camtasia.
Consider this free image overly utility. It hasn’t been updated since 2008.
I find it’s controls to be a little clunky and awkward to work with. However, it took me less than 10 minutes to figure out how to place this PNG image on my screen. All I had to do was create a separate folder in place an image in. Then I pointed the utility to that folder. I chose my desktop as the folder location. Which if I were going to use this utility on a normal basis. Would not be my choice as a location to save image folders to.
It can do animated PNG sequences as well. I realize that's not what you're after.
But that's a feature that some might find useful.
You can also adjust the opacity and scale of the image. I had to reposition the location and scale of the image by quite a bit. I left the opacity at 100 percent.
I prefer another program called ImageOverlyUtility. But it is no longer available anywhere that I can find on the Internet. It was available for free for years. Then offered for sale for five dollars. Then disappeared into obscurity shortly thereafter. It was much easier to work with than this particular program. I still have the program, but it’s illegal for me to share it with others.
This program seems to do the trick and that’s all that really matters. 90 percent of all free image overlay utilities have vanished from the market for some reason over time. This one is available and actually functions. I’m using Windows 10 and it seems to work just fine. Bear in mind I just downloaded it a few minutes ago so I haven’t tested it much.
you may want to give it a whirl and see if it suits your needs.