Reducing noise to the shot-noise limit is a challenge for laser development for ultrasensitive applications in precision sensing and fundamental science. We use hollow-core fiber in a collinear-balanced-detection scheme to suppress 2.6 dB of amplitude noise to within 0.01 dB of the shot-noise limit, while simultaneously preserving the spectrum and temporal profile of picosecond laser pulses. We also provide an enhanced version of the scheme that concatenates multiple circuits for suppression over many frequencies and broad frequency ranges. We perform a first demonstration of this method and reduce total excess amplitude noise, between 2 and 6 MHz, by 85%. These demonstrations enable passive, broadband, all-guided fiber-laser technology operating at the shot-noise limit.