Interesting boat! Welded aluminum makes me believe that strength won't be an issue.
The answer is, it depends. How often are you likely to deploy / retrieve? How big a dinghy are you contemplating? With motor? Are you single-handed? Do you need to trailer it - or perhaps rack store it - where height is an issue?
The logical place to mount a davit with winch is on the side deck, but it looks like your side decks are already narrow. It would be easier to deploy & retrieve single-handed with an electric winch with wired remote - then you could use at least one hand to maneuver the dinghy to keep it from striking the superstructure. Also, a single davit would restrict you to launching on that one side.
I also note that you have a single OB, and the alternator isn't going to put out much power - so an electric winch could put a strain on your electrical system.
A small mast would look "salty", but come with lots more complexity in terms of rigging, options for mounting lights and antennas, et cetera. But my gut feel is that your house is too short to make use of a mast with a dinghy that's likely to run 9' long.
Another alternative you might consider is simply winching it straight up over the stern and over the rear of the house, possibly with an intermediate support. If you are thinking a non-RIB inflatable, that could be the simplest. Heck, since you'll probably take off the OB first, you might be able to just haul it up by hand - I was able to do that with a 2.81 Avon onto a CD22. It was an effort, but certainly doable.
BTW, you might want to ask this on the CBrats site: the folks there own other trailerable cruisers in your size range and might have additional input.