For replacing an adapter four conditions are important:
- The voltage of the adapters should be the same (or within spec range), mostly around 10%.
- The current that can be delivered by the adapter should be AT LEAST the current from the original adapter. The device will use current and gets it from the adapter. If the adapter is not capable of delivering it, than problems occur (not working, smoke etc).
- The polarity should match (+ and - on the inner/outer pin). Some devices have a protection for this, some do not. So do not take the risk.
- The size (length/diameter) of the plug should be same (trivial), otherwise it does not fit.
The wattage is just the multiplication of the current and voltage. Mostly there is a safety margin, but even than with the above conditions you should be ok.