Solid-state amps tend to do better with higher impedance loads. So if you have a stock speaker of 8ohms, going up to a 16ohm speaker will be of little consequence. The only consequence you will have is a reduction in wattage. A 30-watt amp at 8ohms would drop to about 15 watts with a 16ohm speaker. That halving of power doesn't cost you much though, only about -3db. Most people can barely tell the difference when a 3db change in output is made. And this assumes that your 16ohm speaker has the exact same sensitivity as your 8ohm one. If your 16ohm speaker is 2db more sensitive, you may have the same overall SPL as you did with the 8ohm speaker.
For example: Let's assume your 8ohm speaker has a sensitivity of 96db at 1 watt 1 meter. This means with 30 watts of power it should produce about 111db. Each doubling of power adds +3db to the output of the speaker. So at 1 watt you have 96db and at 2 watts you will have 99db, so on and so forth. If your 16ohm speaker has a sensitivity of 98db at 1 watt 1 meter, at 15 watts it will produce roughly 110db. In this case, your 16ohm speaker would have essentially the same output as the stock 8ohm one.
The big takeaway is that watts do not equal output, the sensitivity of the speaker does. Solid-state amps usually have a minimum impedance that they can operate at. It is mostly because of heat and distortion. The lower you go in impedance the higher the THD of the amp will be. Higher impedance speakers tend to sound better with solid-state amps because it reduces THD and improves the ability of the amplifier to control the movement of the speaker.