Does a broken screen on a Nexus One automatically mean the touch screen digitizer needs to be replaced? After 5 years of faithful service, my Nexus One finally cracked (literally) today when it fell from my vehicle. The screen is severely cracked but remains intact in the frame and the display has no problem at all (other than the obstruction by the fractured glass itself). Even touch sensitivity seemed to be intact though I have to risk my fingers on the broken glass to use it. 

From some googling, it seems like touch screen digitizer is the part that's recommended to be replaced in such cases. Will that have to be the case here too, or since the touch sensitivity is intact can it end up a cheaper replacement than that? The digitizer seems to be >$25 here in India and I'd prefer not to spend that on an old soon-to-be-replaced phone.
Screen protector might help protect your fingers, if glass is even and no missing pieces