I can see why you came up with the two possible options. In the bottom photo I submitted if you first click on the view full size in separate window and then zoom in it's pretty clear, maybe that will help identify it.  He does have the shorter antenna of the carpet beetle and the size is about right, being half the size of a pencil eraser,  however it's back was more like a shield bug in that it wasn't oval  it had more of the hexagonal flat surfaces that form into the oval-ish shape,  not smooth.  Also the pattern on its back doesn't fit with what I have been able to find on the carpet beetle,  so my question is,  do carpet beetles have a smooth oval shape back, or do they sometimes have the hexagonal type stink bug/ shield bug?

PS. I apologize if you were already opening in the separate window before zooming, I was not at first because I didn't think it would make it zoom any closer than I was already able to sooooo,  I eventually did and was surprised at how much better I could see him!  So I apologize if you already were doing it that way,  I don't mean any disrespect.  The last photo is the clearest, the second photo shows a black and grey striped leg and with the grey being on the bottom, his feet. Also note the ball on the tips of his antenna, I also do not think it had wings and could fly,  pretty sure he was just a crawler.  Hope this additional information helps to narrow it down.  To me the differences in a carpet beetle are,  it has no wings,  it has a striped leg,  the shell isn't smooth,  possible antenna differences, differences in the stink bug are shape,  coloring,  legs,  antenna.  thanks!