I need to replace a non-polarized electrolytic with a ceramic disc capacitor, can I do that? If not, is there other ways to replace it?
Non-polarized capacitors are supersets of polarized capacitors. Polarization is not a issue when replacing a electrolytic with a ceramic.
In general, you can replace a polarized capacitor with a polarized or non-polarized capacitor with the same capacitance, and with a voltage rating of the original or higher. Non-polarized capacitors may only be replaced with other non-polarized capacitors, unless you know the circuit will only ever apply voltage in one polarity.
In a few unusual cases, the circuit be relying on the electrolytic having some minimum ESR. A ceramic won't work then because those have very low ESR. This is unlikely, but not totally unheard of. There have been power supplies that relied on a minimum out cap ESR for stability. You are less likely to run into that in newer designs, now that ceramics are readily available with 10s of µF capacitance.