In my opinion, I'd suggest the following for a day trip:

Other than the cost of renting a car, if you want to bop around to your own choice spots for the day, absolutely you can rent a car. It's not hard to drive there if you can deal with hills and narrow roads, get an automatic if concerned. Getting lost isn't an issue, very easy. Personally, a Suzuki Jimney (compact 4wd) is great. Easy to maneuver and if you get a rain shower, the 4wd is nice for getting around on the hills. Parking is mostly only an issue in Gustavia, and off season, I wouldn't worry.

We took a tour the first time we visited for a day trip many years ago, figured our time was too short to enjoy spots we wanted to visit (like Saline) so we bailed out and walked (mistake!).

Here's a thought, get a little of both sides of the St. Barts experience by spending a few hours on Saline, then spending a few hours at St. Jean beach (try Tom Beach Hotel beach), and get a the tropical paradise scene and the "scene". From there its an easy shot to get to either the airport or the ferry. (Again, if you can, I'd take the plane on St. Barths Commuter, it's so quick and not much more $)

Alternatively, as long as I'm spending your money, spend a night! There are a couple of guest houses that are reasonable. Then you won't feel so much time pressure and could still take the ferry to offset some of the cost.

We always extend our SXM trips with 4 days or so on SBH because its such a nice change of pace for us.

Have fun! Cheers!