We demonstrate an efficient scheme to accelerate the self-similar pulse evolution and reduce the intensity noise of a free-running femtosecond fiber amplifier based on the pump wavelength optimization. Experiments and simulations indicate the enhanced tolerances of the pulse self-similar amplification to the seed signal power and pump wavelength fluctuations, with the optimum 915 nm pump wavelength. ∼20% increase in the compressed pulse quality and ∼31% reduction in the amplifier root-mean-square (RMS) relative intensity noise (RIN) (1.5 kHz to 5 MHz) have been observed, even with a more than 4 times higher pump laser diode (LD) RIN than the case of 976 nm. ∼50 fs transform-limited pulses are generated with the ∼0.03% amplifier RMS RIN. The proposed scheme can lower the requirements of low-noise self-similar femtosecond fiber amplifiers on the power stability of the seed oscillator and the thermal control of the pump LD, thus denoting potentials for the various satellite-based high-precision applications of femtosecond laser in space.