Can a fish change its density?

Indeed it does. Deuterium, a heavy Hydrogen isotope weighs roughly twice as much as ordinary Hydrogen, and Tritium, the other hydrogen isotope weighs roughly thrice as much. [1H, 1.007; 2H, 2.014; 3H, 3.016.]

There is a small discrepancy due to 'binding energy'.

As far as ordinary radioactive isotopes are concerned, they lose mass when they eject a particle. Some of this mass is the ejecta, some is the 'binding energy'.