"Is there a reason not to use a small flexible antenna from a hand held
radio for the 121.5/243Mhz ELTs?"

Yes. A small flexible antenna will not radiate as strong a signal. A full
size 1/4 wave antenna is about 24" long. When you are lost and someone is
looking for you, you would like to have a strong of signal as possible.

If you are planning on landing a few miles from the search aircraft, the
rubber duck will be fine.

Colin