How to remove trim caulk orange peeled wall
How do you plan on not painting if the new trim is lower than the old trim?  Personally, I'd go with the same if not larger trim to hide any imperfections left by the old trim, but maybe that's just me.

To remove old caulk, just use the flat edge of the painters multi-tool to scrape it away.  Be careful not to dig into the wall or pull up the paper from the drywall.  For anything left, sand it down.  You'll probably want to have some extra drywall mud or spackle available to fix any spots and to cover any screw/nails that were previously covered by the old trim.

And then, yes, you'll need to paint.  It's easier to do a first coat on the trim and the walls before installing the trim.  Then all you have to do is touch-up any nail holes or scrapes.