"Ham-fisted" is certainly more common in Britain, but I have also heard "ham-handed" as well (although not for a large number of years, I have to say.)

In Midland England, where I lived for twenty years, the usual expression for clumsiness was, "caggy-handed." (Older folk said, "cack-handed" but that was looked on as rude by the surprisingly prudish younger generation!) In the north of England, I have heard, "that's a left-handed way of doing it!" According to the context of its use, this phrase can mena either clumsy, or "not the easiest way to go about the job."