Is there any way to set a keyboard shortcut to emulate Ctrl + C when some text or objects are selected, and Ctrl + V when none is? Pasting the clipboard on the top of something wouldn't be possible. It should be easy to code, but I'm curious if there exists some programs that can do it out of the box.
AutoHotkey Edit: updated link, thank you, John Y
It is a sophisticated scripting language with an abundance of conditional checks. I am an intermediate level user of AutoIT, and while it does have some conditional checks, I don't recall seeing a check such as
If any text is selected in active window Then send CTRL+C Else send CTRL+V
But I've also not looked for that kind of conditional check before. I have seen powerful conditional checks in AutoHotkey before, however, even though I have not written scripts with it. My experience has been that I have used a few scripts designed by other people.
If I could go back in time to when I first found AutoIt, I would wish to learn AutoHotkey instead. (But that might be because the grass is always greener on the other side of the logic gate. Ha!)
To directly answer your question in the narrowest sense, I am unaware of any clipboard management software that does what you are seeking, but I have also not needed clipboard software since Windows 95!