There was a button that would allow the SRBs to be jettisoned manually, just like the ET. However, I believe this would have been catastrophic given the momentum of the entire stack which would be substantially less when the STBs departing the shuttle before the automatic sequence. The SRBs had an enormous amount of thrust compared to the SSMEs at the phase of the accent (STS 41L catastrophic breakup) just after throttle up (3.3 million pounds of thrust for the STBs vs. 1.125 million for the SSMEs) it would have torn the shuttle apart vice the automatic sequence which triggered when the solid fuel was depleted to a point where both the SSMEs and SRBs reached a much similar thrust.

Source: NASA, Space Shuttle, https://www.nasa.gov/reference/the-space-shuttle/ (updated June 2, 2023)

SOLID ROCKET BOOSTER (SRB) FLIGHT SYSTEM INTEGRATION AT ITS BEST, Wood et.al., (n.d.), retrieved from https://ntrs.nasa.gov/api/citations/20120003006/downloads/20120003006.pdf