Hi andreas,
Don't cut those figs as they are of no use to you yet, but will help the next crop that will be of use to you and your figs .
If you're not looking into breeding fig trees, go ahead but .
But this is not the better time to do it, IMO . I would do the airlayer in June or July (perhaps May at your location) .
If there are root-shoots, I would try to take some.
Or simply take cuttings with no figs, as nevertheless, the rooting cuttings won't have the roots to keep those figs up and alive.
I would try to find the caprifigs with the more figs. If this is the one in your neck of the woods, then take cuttings on that one .
What I would do, is take branches in June or when the wasp is actively seeking new figs in your climate and put those in bottles of water in a shady spot under your fig trees.
The wasp would then be released directly near your figs at the right time for the pollination and if the branches root, you'll have caprifigs for you at the same time.
Of course, it all depends on your access to that tree. If you don't have easy access to that tree later in the year, then take the opportunity you have now, and do it now .
Good luck !