Re: INSTALLING GARMIN 140 FISH FINDER transducer ?
http://www8.garmin.com/manuals/1069_OwnersManual.pdf
According to the manual, the mounting options for the transducer that comes packaged with the 140 are on the trolling motor, or on the transom itself.
Garmin offers various thru-hull transducers:
https://buy.garmin.com/shop/shop.do?cID=149&pID=344#Transducers
However, the installation of such would obviously require drilling a hole thru your hull.
I have a Hawkeye depth sounder made by Norcross Marine that uses a transducer that can be mounted in the hull or on the transom. The entire kit was around $70. I have tested the transducer in both locations with similar results.
http://www.hawkeyeelectronics.com/products/D10D/overview.htm
Norcross also offers a great transducer exchange program that allows you to exchange their transducers free of charge for one that will operate with your setup.
You could try one of their transducers with your Garmin cable plug and if you could get the wiring correct, it may work with your fish finder. I'm not too sure of this, however if you are dead-set on having the transducer mounted inside the hull then it may be worth the time, effort, and experimentation.
Why not just mount the one you have on the transom like most folks?