So are we - but this year's figs are already visible as lentil sized buds before the leaves appear. These are the ones you will lose by pruning.

One of our figs is just thinking about uncurling its leaves, the other hasn't started yet.

At this time of year I'd be worried about sap bleeding, so if you are going to prune, test a small twig first. But you're obviously OK about taking out dead stuff.

That said, commercial growers prune heavily, taking out big branches, in order to encourage a lot of branches since, as has already been said, figs tend to fruit at only at the tips.

So if you think you are still OK to prune, then seizing the opportunity to cut back a few branches may give you more figs next year.

(There again, if there are a lot of embryo fruits coming, I'd find it very hard to prune - delayed gratification isn't my thing as far as figs are concerned.)

Figs are very tough things. April two years ago last my garden waterer forgot about the potted fig, which lost all its leaves and died back. I chopped it back to 6 inch apparently dead twigs and parked the pot under a shrub to deal with later. In late August it produced a whole bunch of new leaves and is now going fine.