"Can I change only the crystal of an oscillator circuit to change its operating frequency?"
There are many types of oscillators that are frequency controlled by a crystal. In some of them, such as those that do not use additional tuning circuits (coil in parallel with a capacitor) to transfer the signal or even to make the feedback, the simple exchange of the crystal is sufficient, as long as the basic component (transistor or tube) is able to oscillate at the new frequency. However, in circuits that have inductors such as a load or resonant circuit, it may be necessary to change these circuits or adjust it if the new frequency is different from the original.