What's the hazzard of going from a 20gage wire to a 15 gage wire when installing an emergency exit light

Well it is over kill.

14 AWG conductors will work, but it would be smarter and easier to work with the 20 AWG wire.

Now if you really meant 12 AWG conductors, then the answer is much clearer.

If you splice 12 AWG wire to 14 AWG wire, then you must protect the entire circuit with a 15 amp breaker.

You cannot use a 20 amp breaker with 14 AWG wire in the circuit,

Exactly where will this #20 AWG wire be installed?

Minimum size building wire allowed will be #14, minimum size wire used in a fixture would be #16.