Shot-noise-limited laser operation over a wide spectral bandwidth is demonstrated by using a semiconductor active medium inserted into a high-Q external cavity. This approach ensures, with a compact design, a sufficiently long photon lifetime to reach the oscillation-relaxation-free class A regime. The laser relative intensity noise is limited to the shot-noise relative floor, $-156\mathrm{dB}∕\mathrm{Hz}$ for a $1\mathrm{mA}$ detected photocurrent, over the $100\mathrm{MHz}\text{to}18\mathrm{GHz}$ bandwidth. The optimization of the laser cavity is discussed, and convenient shot-noise-limited operation is shown to be a trade-off between the cavity length and laser mode filtering.