The 'right' way to do it is likely to use a tape bulk eraser - You're likely going to want a handheld model for cost reasons, though specialised models for dat probably exist. These seem to be very rare at the moment. Most of the ones I'm finding on the internet are desktop models and insanely expensive.
A quick bit of research on google suggests that they work on DAT tapes but not LTO.
However, considering the impossibility of verifying that the tapes have been properly wiped, I may suggest physical destruction. I wouldn't feed these in a shredder (they may clog up teeth designed for paper, even if you shuck the tape and just feed that in), and most other ideas I can think of seem risky. Maybe it'll blend
I'd consider checking to see if there's a commercial operation locally that would securely dispose of these for you instead, especially if its a one off thing. Even if its more expensive, it'll ensure you get it done the right way.
This spiceworks thread has a few ideas - some worse than others
- Cutting up the tapes by hand - seems timeconsuming (I wonder if an angle grinder would do a good job mangling the tapes)
- Microwaves (seems horribly risky)
- Encasement with concrete
- Bleach (how would that even work?)
- VERY strong/large magnets (May work, but the bulk eraser uses a varying magnetic field, not a static one).