Due to real estate/space constraints, I want to put a Printer icon on a button rather than the text "Print"
Yet I see no obvious way to do that (No "Image" property or so on the button).
Is it possible (without jumping sideways through flaming hoops)?
The standard button does not support images, no. You have to create a custom control. This was such a common request that Microsoft released an article on MSDN showing how to do it.
I'd argue that they would have been better served just creating the support in the Button (after all, they had several releases after that article) but they didn't ask me.