Yes, you could buy a transducer made for ice fishing, If you don't have an extra around. Or buy an older unit of the same brand your running so you can transfer waypoints/ and map card and modify the transducer. Or make a wooden base that holds the unit, has a swing arm that is adjustable that you can easily adjust the cable length/arm for the depth ice your fishing. Depends on your requirements. The battery concern again depends on your mode of transport out on the ice, hours of use etc.
Like mentioned, a flasher always is a "real time" and very accurate sounder that can mark fish in the weeds. I love em. If you can afford both, go for it. The GPS with waypoints is very helpful just like soft water. IMHO