Is it okay to use a power supply that provides slightly more voltage and amperage than what's rated?
The weird symbol indicates its a DC output. This laptop adapter supplies an output voltage of 19 V and a maximum output current of 3.42 A, well above your original adapter's 2A maximum. This doesn't mean your device will consume 3.42 A when its powered with this adapter; it is only an indication of the maximum current that can be drawn through the adapter by any device that it is connected to, above which the adapter gets damaged. Any device will only draw as much current as it needs, so long as its power source can supply it.

However, the laptop adapter's voltage is a full volt above the specified 18 V; this will cause more current to flow into your device, since the voltage has been increased. Whether this difference is significant enough to destroy your LED sign is a matter of how much tolerance was built into it; the 1-volt increase may merely increase the brightness of the LEDs or burn them, if 19 V is outside the device's range, or have no noticeable effect at all (if the 19 V is being stepped down further within the device). 

TLDR, don't try using this adapter unless you are willing to risk damaging your device from the extra current.