Uncertain. Suggested by lexicographer Sidney Baker to derive from speiler, via eeler-spee or eeler-speeler by pig Latin, and from which illywhacker. The verb form whack the illy is a back-formation from the noun.
Alternative forms 
illywhacker (plural illywhackers)
- (Australia, colloquial, obsolete) A small-time confidence trickster or seller of trinkets.
Usage notes 
The term is long obsolete and the exact original sense is thought to be lost.