Don't waste your time.
Go to USkidsgolf.com, they have clubs for kids. The problem with cutting down adult clubs is that a normal golf club head is pretty heavy. When the length of the shaft is cut down but the head weight is not reduced it makes it extremely difficult if not possible for a kid to control. They will struggle just to make contact. The US Kids clubs have smaller heads, smaller grips and are weighted appropriately for the length of shaft. Entire sets can be a little spendy at $120 or so, but you can buy individual irons for around $25 a piece or so.
Forgot to mention, the US kids sets are based on child height. Takes all the guessing out of finding the right length shafts.