I wouldn't be surprised to find that they can't be changed.
What end result, exactly, are you trying to produce? It may be possible to put a graphic object with your desired arrow on top of the field or even put a "no browse mode access" copy of the field with one of the two formats on top of the other with the other value list format so that it looks like a pop up menu but is actually a drop down list or vice versa.
These aren't exactly pretty solutions, but they might work.
For my tastes, the background color of the "rectangle" where the drop down arrow appears is too dark, so I wanted to choose a lighter color. Definitely not a deal-breaker. I just wanted to be sure I wasn't missing a control somewhere that gave me that flexibility. Thanks!
Going back a ways to this thread, but I was looking for something similar recently. For your issue, ABucthel, I believe that you can now do this in FMP 14.
Pick the field you want to style
Choose Appearance in the Inspector
Change the box where it says 'Pop-up menu' to 'Pop-up menu button'
This will let you style the background color at least. You can style the icon color by setting it to 'Pop-up icon'.
However, you still change seem to directly change the icon itself (e.g. size, shape), nor even just select to show/hide the icon (like you can for a drop-down menu).