Yeah right (marker). PITA but I cut out the critical info with scissors then trash these small pieces, then the bulk of the stuff can go to recycle without shredding. The key is to do this regularly without letting it stack up.
Maybe use them for fire starter.

Ummmm. no. Because someone who tries hard enough can still pretty easily get that information. If anything, do BOTH since someone determined enough can get it with shredded paper too. So, if you have a criss cross shredder, mix the shreds up really well, and then put a handful or two in different bags. Put out on different days. OR at different addresses.

FYI you can still read the writing under the blacked out area

our recycler accepts shredded paper only if in a clear plastic bag

is paperboard recyclable