In my experience figs are pretty tough. I've ripped up trunks that were growing where I didn't want them to, put them in pots with almost no roots, and they survived the butchering. Cuttings taken from the semi-green growing tips also root very readily. This might be a good place to start if you are unsure about uprooting it and want to guarantee something survives. Are far as I know, air layering should work too, but I've never done that personally.
If you opt to dig it up, yes, cut it back to help it recover. ---Although if it's already dormant when you dig it up, cutting it back is less on an issue. If it's leafed out when you dig it up, it'll drop those leaves anyway to reduce moisture loss until it grows new roots. So, cutting it back does the same thing, but saves the tree a little extra moisture loss/stress.