"Normal" LEDs should work fine, but any that use a phosphor to change the light output spectrum (like most white ones) may be visibly slow cutting off in a high speed application. (I have no idea how slow though)
An RGB LED with separate terminals for each colour could probably be used to give white, using appropriate resistors for each element to balance the colour levels? Or separate high output R,G & B ones.
Most LEDs can work fine on somewhat higher currents in low duty cycle applications, such as multiplexed displays - or this. Check the manufacturers data sheet for the pulse ratings.