Diode rating
The diode is only going to have to be able to carry the current absorbed by the coil of the relay, I would guess this to be less than 100mA (most relays are 20mA or so).
So as long as the diode you intend to use is a signal diode and not a zenner diode, and has a low dropout voltage (0.6 for silicon, or 0.4 for Galium), and can handle several 100mA then it should be OK.
To make sure you would have to measure the current on the relay coil to see what they draw typically.(put a meter in series in A mode and see how many amps are drawn).
The only other disadvantage of using a diode with thinner wires is that they will not be as sturdy, mechanically.
Generally most components are over specified so that they do not run at the extremes of their characteristics, so without more info on the diodes you intend to use I can't help any more than this.
Pete (simples, 'innit)