Direct sequence spread spectrum (DSSS) signals possess strong and undesirable cyclostationary features when used in covert communications. This paper addresses their mitigation via chip-wise faster-than-Nyquist (FTN) signaling and time-varying pseudo-random SNR-optimal spreading sequences. We append a differential phase-shift keying (DPSK) encoder to the DSSS/FTN system to use a non-coherent differential receiver that facilitates carrier synchronization in challenging scenarios involving phase, frequency, and frequency-rate offsets. The proposed DSSS/FTN system proves robust with a bit-error-probability performance close to its traditional DSSS/Nyquist counterpart. Our results pave the way for designing low probability of detection/intercept waveforms without incurring a noticeable extra complexity at the receiver side.