Cordless will not be lighter. Lithium or not, that battery has weight.

Also, you should consider how frequently you're going to be using the tool. Batteries aren't eternal, so if this is a once-a-year thing, corded is probably more practical so you don't have batteries dying on the shelf.

While cordless is very cool and handy, personally I'd save the money, run the extension cord, and buy a whole other thing with that $160.