I would always rather putt, but that doesn't mean I would putt in this scenario. As others have mentioned there is not enough information to make a specific judgement.
From off the green a good putt and a good chip will have the same result, but a bad putt will usually end up closer than a bad chip.
In this case it wasn't a lucky skip, it ended up at least 20 yards past. But, the driver will eventually be the right club. Right now, if I want to shoot 90 or less, I need to take double out of play as much as possible, I think. It's so hard to get those back. And going over the fence is almost certainly double, if not worse. If I was good at the game, and trying to shoot 80, then trying to take advantage of the birdie hole would make sense. Maybe I am being too defensive right now? Or maybe that's where my game is? It's a bit of a conundrum. But I appreciate the feedback!