I use both a billhook and a sickle from right to left - across my line of axis, but not towards me. Often a billhook is used in a downwards motion, in which case it should be used outside the line of the body - i.e. to the right of a right-handed person. If possible it should be used back hand, i.e. away from the body. However, much depends on the task...
In medieval pictures of vine pruning the blade is shown facing the user, however it is not used with a chopping motion, but pulled towards the user with a paring or slicing cut...
European sickle users often wear finger guards, made of wood, or sometime leather, and my late father-in-law, a retired English farmer, always wore leather gaiters to protect his shins