I don't think so.
You could change the crystal, but the complier would be expecting 16MHz and that would mess-up any timing in your firmware. (i.e. delay(1000) would delay for 2 seconds.) I don't if there's a compiler option for an 8MHz device (that would solve the timing issue), but there would probably be something else device-specific that would get messed-up if you use the wrong compiler-option.
For the actual hardware (a remote controller)
Processor speed shouldn't be an issue in that application.