If you look over the datasheets, note that the forward voltages for each of those diodes are specified at different forward currents. The MMSD4148 has a 1.0V forward voltage for a forward current (I_f) of 10mA. The 1N4148W has a forward voltage of 1.25V but at an I_f of 150mA. Deeper in the 1N4148W datasheet they list a forward voltage of 0.855V for an I_f of 10mA, so the 1N4148W actually has a lower forward voltage drop. Maybe the MMSD4148 actually has a lower forward voltage drop at 150mA, but since Fairchild didn't see fit to provide any other I_f specs or curve for its forward voltage compared to I_f, I couldn't tell you.
As for whether or not the voltage drops will matter, are you building this keyboard yourself or are you repairing an existing one? I haven't cracked one open to see if it has diodes on every key... I would assume all a commercial keyboard would do if it has diodes on every key is to give some indication for which key is pressed. Maybe a bunch of pullup resistors on buffer inputs where a keypress connects the cathode of the diode to ground and takes the input of the buffers low. Something like that... See the circuit below for what I mean.
My guess is that the 1N4148W should work just fine.
If you're building the keyboard yourself, maybe show us the schematic and we could give you a better answer?