Re. giving the succulent a haircut- with any plant that has a lot of woody growth at the base and leaves only at the tips, prune gently to start with. Often there's dormant buds in the woody growth that will start to grow once the tips have been cut back, but sometimes the buds are dead, not dormant. If they start to shoot out nicely after a few weeks, then prune back harder to encourage the new shoots.
You could give yourself some "plant insurance" by taking a few cutting sized pieces off the succulent. Leave them to dry off for a few days to a week, then put them into just-damp sand. Succulents store so much moisture in their leaves and stems that the cuttings often rot if they're put straight into sand without the drying off time.
