GLBA section 501(b) governs this and is pretty broad and vague. There are several interpretations readily available, including the FFIEC IT Examination Handbook. Nothing that tells you "must be a crosscut shredder" or anything that specific. Historically, my examiners and auditors have asked about and strongly recommended using the best quality shredding we can and to include what type of shredding we are using in our risk assessment as a mitigating factor.
_________________________
"Gratitude makes sense of our past, brings peace for today, and creates a vision for tomorrow." - Melody Beattie