Well, slithy, it looks like we've hit on one of those classic "origin unknowns" (see "the full monty" or "the whole nine yards")...but it's seems to have Celtic roots, and is listed in the Dictionary of Dublin Slang and Phrase http://homepage.tinet.ie/~nobyrne/s.htm

Here's what Merriam-Webster's says:

Main Entry: she·nan·i·gan
Pronunciation: sh&-'na-ni-g&n
Function: noun
Etymology: origin unknown
Date: 1855
1 : a devious trick used especially for an underhand purpose
2 a : tricky or questionable practices or conduct -- usually used in plural b : high-spirited or mischievous activity -- usually used in plural